- A 10 meter ladder is leaning (#759)
A 10 meter ladder is leaning aganist a building. The bottom of the ladder is 5 meters from the building. How many meters high is the top of the ...
geometric proofs, pythagorean theorem, triangles, right triangles, polygons, shapes, plane figures, curves
- A 12-ft. ladder is leaning against a building (#3547)
A 12-ft. ladder is leaning against a building. The bottom of the ladder is 7 ft. from the ...
triangles, curves, plane figures, shapes, right triangles, polygons
- A 20-ft ladder is leaning against a wall (#2485)
A 20-ft ladder is leaning against a wall. If the ladder is 12 ft from the base of the ...
pythagorean theorem, right triangles, triangles, polygons, shapes, plane figures, curves
- A 32 foot ramp connects a platform with a sidewalk (#2504)
A 32 foot ramp connects a platform with a sidewalk that is at ground level. if the platforn is 6 feet above ground ...
triangles, curves, radicals, numbers, number sense, right triangles, pythagorean theorem, plane figures, shapes, polygons
- A 7m ladder against the wall of a building (#1139)
A 7m ladder against the wall of a building and its foot is 2m from the base of the ...
plane figures, shapes, polygons, triangles, pythagorean theorem, right triangles, curves
- A birthday present is packaged in a tube (#1683)
A birthday present is packaged in a tube that has a length of 10 inches and a diameter of 4 ...
circumference, solid figures, cylinders, area, surface area, shapes, curves, circles, plane figures
- A cable of a suspension bridge is in form of a parabola (#3165)
A cable of a suspension bridge is in form of a parabola whose span is 40 m. the roadway is 5 m below the lowest point of cable. If a extra support is provided across the cable 30 m above the ground level, find length of the support if the height of the pillars are 55 m
parabolas, curves
- A circle with radius 5 (#261)
A circle with radius 5 has its center at (4,1). the line x-2y+4=0 intersects the circle. find the intersections
circle equation, circles, equations, plane figures, shapes, curves
- A clubhouse has a roof (#3080)
A clubhouse has a roof whose slant height is 13 m and base is 24m. Two extra supports 2m and 3 m from the peak and perpendicular to the base of the peak need to be ...
similar triangles, triangles, polygons, shapes, plane figures, curves
- A dog pen is in the shape of a right triangle (#2653)
A dog pen is in the shape of a right triangle. The longer leg measures 15 feet. The hypotenuse is 7 feet shorter than three times the length of the shorter ...
pythagorean theorem, right triangles, triangles, polygons, shapes, plane figures, curves
- A guy wire reaches from the top (#2005)
A guy wire reaches from the top of a 39.32 ft pole to a point on the ground 15' from the ...
pythagorean theorem, radicals, triangles, number sense, numbers, polygons, shapes, right triangles, plane figures, curves
- A ladder 39 feet long leans against a building (#1419)
A ladder 39 feet long leans against a building and reaches the ledge of a window. If the foot of the ladder is 15 feet from the foot of the ...
trigonometric functions, cosine, right triangles, pythagorean theorem, triangles, polygons, shapes, plane figures, curves, functions
- A ladder 39 feet long leans against a building (#2869)
A ladder 39 feet long leans against a building and reaches the ledge of a window. If the foot of the ladder is 15 from the foot of the ...
right triangles, pythagorean theorem, triangles, curves, plane figures, shapes, polygons
- A ladder leans against the side of a building (#3493)
A ladder leans against the side of a building. The base of the ladder is 5 metres from the building, and the top is 12 metres above the ...
triangles, plane figures, shapes, polygons, right triangles, curves
- A ladder reaches a height of 64 feet on a wall (#3530)
A ladder reaches a height of 64 feet on a wall. if the bottom of the ladder is placed 4 feet away from the ...
pythagorean theorem, right triangles, curves, shapes, triangles, polygons, plane figures
- A large pizza has a diameter (#3431)
A large pizza has a diameter 35cm. Two large pizzas cost $19.99. A medium pizza has a diameter 30 cm. Three medium pizzas cost $24.99...
radius, circles, curves, shapes, plane figures, area of circles, area
- A man on a 135-ft vertical cliff looks down (#2873)
A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his ...
pythagorean theorem, sohcahtoa, trigonometric functions, trigonometric identities, right triangles, plane figures, triangles, curves, shapes, polygons, functions, identities
- A mirror in the shape of a paraboloid (#2784)
A mirror in the shape of a paraboloid of revolution. If a light source is located 1 foot from the base along the axis of symmetry and the opening is 2 feet ...
parabolas, curves
- A road up a hill makes an angle (#3220)
A road up a hill makes an angle of 5.1 with the horizontal. If the road from the bottom of the hill to the top of the hill is 2.5 miles ...
right triangles, triangles, polygons, shapes, plane figures, curves
- A running track has straight sides and a semicircular ends (#3339)
A running track has straight sides and a semicircular ends. If the length of the track is 440 yd and the two straight parts are each 110 yd ...
curves, shapes, plane figures, circle equation, circles, equations
- A sail is in the form of a right triangle (#2429)
A sail is in the form of a right triangle that is two times as high as it is wide. The sail is made from 4 square meters of ...
triangles, polygons, shapes, plane figures, curves, right triangles
- A sailboat has a triangular sail (#1195)
A sailboat has a triangular sail with an area of 30 square feet. the height of the sail is 7 feet more than the length of the base of the ...
triangles, area, shapes, polygons, plane figures, curves
- A sailboat has a triangular sail with an area (#1407)
A sailboat has a triangular sail with an area of 64 square feet and a height of 16 ...
triangles, area, shapes, polygons, plane figures, curves
- A semicircular window is to be laminated (#2402)
A semicircular window of radius 12 inches is to be laminated with a sunblock coating that costs $0.75 per square inch to apply. What is the total cost of coating the ...
curves, shapes, circles, circumference, plane figures, area
- A ski resort is installing tows (#2364)
A ski resort is installing tows on its new ski runs. One hill has a vertical height of 500m and is inclined at 42 ...
curves, shapes, right triangles, pythagorean theorem, polygons, plane figures, triangles
- A smaller circle rolls along the inside curve (#3460)
A smaller circle rolls along the inside curve of a larger circle. The diameter of the larger circle is three times that of the smaller ...
curves, plane figures, shapes, circles, circumference
- A street that is long is covered in snow (#3197)
A street that is long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn times in traveling the length of the street. What is the diameter of the tire?
Use π = 3.14. Round your answer to the nearest ...
diameter, circles, plane figures, shapes, curves
- A swimming pool is 10 feet across (#2491)
A swimming pool is 10 feet ...
circumference, circles, plane figures, shapes, curves
- A therapy pool in the central high scool traning room (#3004)
A therapy pool in the central high scool traning room is in the shape of a 9 meter ...
area, circles, plane figures, shapes, curves
- AB is one of the direct common tangent (#1085)
AB is one of the direct common tangent of two circles with radius 12 cm and 4 cm respectively touching each ...
circle equation, circles, equations, plane figures, shapes, curves
- AC is a tangent to circle (#3336)
AC is a tangent to circle O at B. BD is a chord. Arc BD=110...
curves, major arc, arcs
- After Mr.Zillmer got hit in the head with a pitch (#1911)
After Mr.Zillmer got hit in the head with a pitch. Mr. Rukamp came up to bat. The equation h=-.004d2 +.96d+3 represents the path the ball took after Mr. Rukamp hit the first ...
parabolas, curves
- An arch is in a form of a parabola (#1633)
An arch is in a form of a parabola which the vertex on the top. if it is 45m wide on the base and 18m high on the ...
curves, parabolas
- At noon, ship A is 150 km west of ship B (#1136)
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h, How fast is the distance between the ships changing at 4:00 P.M.?
triangles, right triangles, pythagorean theorem, polygons, shapes, plane figures, curves
- Determine the distance across the base (#1914)
Determine the distance across the base of a parabolic arch that measures 30 feet at its highest point if the roadway through the center of the arch is 48 feet wide and must have a minimum clearance of 15 feet.
parabolas, curves
- Editor of the school newspaper (#428)
Editor of the school newspaper must reduce the size of a graph to fit one column. The original graph is 2 inches by 2 inches, and the scale factor from the original to the reduced graph is 8:3...
polygons, curves
- Every time the pedals go through (#917)
Every time the pedals go through a 360 degree rotation on a bicycle, the tires rotate 3 times. If the tires are 24 inches in ...
circumference, circles, plane figures, shapes, curves
- Find the area of a right triangle (#3001)
Find the area of a right triangle with legs of length
a = 5 √3 , and
b = 2 √3 + 3 √2
area, right triangles, triangles, polygons, shapes, plane figures, curves
- Find two numbers such that (#1166)
Find two numbers such that their sum is 20 and the sum of their squares is as small as possible.
curves, parabolas
- From a point 12 m from the base of a flagpole (#2655)
From a point 12 m from the base of a flagpole the angle of elevation to the top of the pole is 42 ...
angle, measuring angles, pythagorean theorem, right triangles, triangles, curves, plane figures, shapes, polygons
- From a space probe orbiting Jupiter’s moon Io (#2492)
From a space probe orbiting Jupiter’s moon Io from an altitude of 552 km, it was observed that the angle of depression from the probe to the surface of this moon was 39.7 degrees. What is the radius of the ...
radius, circles, plane figures, shapes, curves
- How far up a wall (#3143)
How far up a wall will a 10-meter ladder ...
curves, shapes, polygons, plane figures, triangles, right triangles, pythagorean theorem
- How far up a wall will an 11m ladder reach (#1000)
How far up a wall will an 11m ladder ...
pythagorean theorem, right triangles, triangles, polygons, shapes, plane figures, curves
- If a ladder is leaning against a building (#2714)
If a ladder is leaning against a building, and the distance from the bottom of the ladder to the building is 8 ft. less than the length of the ladder, how high up the side of the building is the top of the ladder if the distance is 1 ...
right triangles, solving algebraic equations, pythagorean theorem, triangles, polygons, shapes, curves, plane figures, algebraic equations, solving equations, equations
- If a line that passes through points (#625)
If a line that passes through points (-3,-2) and (-2...
curves, perpendicular lines, lines
- If a parallelogram has an area (#3353)
If a parallelogram has an area of 115 square units anda base length of 12, what is the height of the ...
polygons, curves, parallelograms, shapes, plane figures
- If one leg of a right triangle is 8 inches long (#2360)
If one leg of a right triangle is 8 inches long, and the other leg is 12 inches ...
triangles, polygons, plane figures, shapes, pythagorean theorem, right triangles, curves
- If you rolled up a letter size sheet of paper (#1415)
If you rolled up an 8 1/2 by 11 in sheet of paper into the largest possible cylinder 8 1/2 in ...
circles, circumference, plane figures, curves, shapes, diameter, cylinders, solid figures
- In a certain triangle, the second side (#2090)
In a certain triangle, the second side is one-third of the first side in length. The third side ia 2 meters less than the first side. The perimeter of the triangle is 26 meters. Form an algebraic equation to express the problem, and identify the variables,...
triangles, polygons, shapes, plane figures, curves
- Jerry has a window in his room (#2973)
Jerry has a window in his room. His window is a triangle. If angle one measures 63 degrees, and angle two measures 77 ...
angle, triangles, curves, plane figures, shapes, polygons
- Jim’s nephew owns a triangular plot of land (#2980)
Jim’s nephew owns a triangular plot of land. The perimeter fence that surrounds the land measures 121 feet. The shortest side is 15 feet longer than one-half of the longest side. The second longest side is 4 feet shorter than the longest ...
triangles, polygons, shapes, plane figures, curves, perimeter
- John leaves school to go home (#1652)
John leaves school to go home. He walks 100 blocks North and then 820 blocks ...
triangles, pythagorean theorem, right triangles, polygons, shapes, plane figures, curves
- Larry bought a trampoline (#3423)
Larry bought a trampoline measuring 10 feet by 12 ...
triangles, plane figures, shapes, polygons, curves, right triangles
- line segments (#244)
on segment wz if wy equal 21 and xz equals 26 and yz is twice wx what is the value of xy
line segments, curves, lines
- Mia wants to build a fence around her yard (#2628)
Mia wants to build a fence around her circle shaped yard. The yard has a radius of 8 ...
circumference, circles, plane figures, shapes, curves
- One angle of a triangle has a measure (#863)
One angle of a triangle has a measure that is 10 more than twice that of the ssecond angle. The third angle has a measure 10 less than the ...
curves, triangles, polygons, shapes, plane figures
- proportional triangles (#910)
Triangle EFG is similar to triangle ...
proportional triangles, curves, plane figures, shapes, polygons, triangles
- Sarah had an idea (#234)
Sarah had an idea, what would happen if you put a golf ball inside a basketball? How much room would there be inside the basketball afterwards. Her golf ball has a radius of 1.68 inches while her basketball has a diameter of 9.4 ...
circle equation, circles, equations, plane figures, shapes, curves
- The answer for the second angle (#2761)
The answer for the second angle in a triangle is three times as large as the frist. the third angle is one third as large as the second angle. Find the angle ...
triangles, polygons, plane figures, shapes, curves
- The area of a circle (#1531)
The area of a circle is 28 square ...
curves, shapes, plane figures, circles, circumference
- The area of a circle (#2300)
The area of a circle is 28 sqaure ...
circumference, plane figures, curves, shapes, circles
- The area of a circle is 30 square feet (#2863)
The area of a circle is 30 square feet. The diameter of a second circle is 2 feet shorter than that of the first ...
circles, area, shapes, plane figures, diameter, curves
- The area of a triangle (#3232)
The area of a triangle is 30in2. The base of the triangle measures 2 in. more than twice the height of the ...
systems of equations, solving systems of equations, triangles, polygons, shapes, plane figures, curves, solving equations, systems, equations
- The base of an 8-foot ladder (#619)
The base of an 8-foot ladder is placed 2 feet away from a ...
pythagorean theorem, triangles, right triangles, polygons, shapes, plane figures, curves
- The circumference of a bicycle (#1664)
The circumference of a bicycle is 50.24 ...
circumference, circles, plane figures, shapes, curves, diameter
- The face of the triangular concrete panel (#2918)
The face of the triangular concrete panel has an area of 45 meters, and its base is 3 meters longer than twice its ...
area, shapes, plane figures, triangles, curves, polygons
- The first Ferris wheel was built (#3125)
The first Ferris wheel was built in 1893 in Chicago. Its diameter was 250 feet. What was the actual circumference of the Ferris wheel? Use 3...
diameter, circles, plane figures, shapes, curves, circumference
- The hypotenuse of a right triangle (#169)
The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less that the longer ...
hypotenuse, right triangles, triangles, polygons, shapes, plane figures, curves, pythagorean theorem
- The hypotenuse of a right triangle (#196)
The hypotenuse of a right triangle is twice as long as one of the legs and 10 inches longer than the ...
hypotenuse, right triangles, triangles, polygons, shapes, plane figures, curves, pythagorean theorem
- The hypotenuse of a right triangle (#934)
The hypotenuse of a right triangle is twice as long as one of the legs and 8 inches longer than the ...
plane figures, hypotenuse, right triangles, shapes, triangles, polygons, curves, pythagorean theorem
- The hypotenuse of a right triangle (#2792)
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the
remaining ...
right triangles, triangles, polygons, shapes, plane figures, curves, solving systems of equations, solving equations, systems of equations, equations, systems
- The legs of a right triangle (#2087)
The legs of a right triangle are 12 and 16 inches long, ...
area, right triangles, triangles, polygons, shapes, plane figures, curves
- The legs of a right triangle (#2651)
The legs of a right triangle are 5 and 7 centimeters long, respectively. What is the length of the hypotenuse? If ...
plane figures, right triangles, pythagorean theorem, curves, shapes, polygons, triangles
- The legs of a right triangle are 12 inches and 8 inches (#2037)
The legs of a right triangle are 12 inches and 8 ...
right triangles, plane figures, triangles, shapes, curves, hypotenuse, polygons, pythagorean theorem
- The length of the hypotenuse of a right triangle (#1267)
The length of the hypotenuse of a right triangle is three times the length of one of the legs. The length of the other leg is the square root of 72...
plane figures, shapes, polygons, triangles, curves, pythagorean theorem, right triangles
- The main suspension cables between the towers (#398)
The main suspension cables between the towers of the Golden Gate Bridge form a parabola that can be modeled by the quadratic function
y=0.000112x2 + 220
where x is the horizontal distance from the middle of the bridge and y is the vertical distance from the water level.
The cables are connected to the towers at points that are 5000 feet above the road, and the road is about 220 feet above the mean water ...
parabolas, curves
- The mainsail of a lightning sailboat (#2883)
The mainsail of a lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24 ft tall mainsail has a leech length of 26ft and if Dacron sailcloth casts $10 per square ...
polynomials, pythagorean theorem, area, right triangles, shapes, triangles, plane figures, curves, polygons
- The mast of a sail boat is 18 feet high (#405)
The mast of a sail boat is 18 feet high and the boom is 15 feet long. The gooseneck can rotate 360 ...
triangles, polygons, shapes, plane figures, curves
- The measure of the largest angle (#966)
The measure of the largest angle of a triangle is 12 degress less than the measures of the other two. The smallest angle measures 58 degress less than the largest ...
triangles, shapes, polygons, plane figures, curves
- The minute hand of a clock (#2955)
The minute hand of a clock is 6 inches ...
curves, plane figures, shapes, circles, circumference
- The minute hand on a clock (#2787)
The minute hand on a clock is 15cm ...
circumference, circles, plane figures, shapes, curves, area
- The radius of a bike wheel is 17 inches (#1280)
The radius of a bike wheel is 17 ...
curves, circles, shapes, plane figures, circumference
- The right angle of the triangle (#2489)
The right angle of the triangle is 1808 feet the slope is 25,2 ...
pythagorean theorem, right triangles, trigonometric functions, plane figures, shapes, polygons, curves, triangles, functions
- The sum of the sides of a right triangle (#2660)
The sum of the sides of a right triangle is 49cm and the hypotenuse is 41...
right triangles, triangles, polygons, shapes, plane figures, curves, pythagorean theorem
- The vertex of this parabola (#1441)
The vertex of this parabola is at (3, 5). When the y-value is 6, the x-value is -1...
parabolas, curves
- The volume of the soda can (#1671)
The volume of the soda can is fixed at 400 cubic centimeters. Use the volume with each radius to find the possible heights of different sized soda cans. Once the height column is completed calculate the surface areas. The results for radius are already given. Round the height to the nearest tenth and the surface area to the nearest whole number. The given radius are: 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 ...
plane figures, cylinders, area, volume, shapes, surface area, curves, circles, solid figures
- There are two similar triangles (#2207)
There are two similar triangles. Dimensions of one are 12,16, 20, and the other's are 12,9,...
similar triangles, polygons, plane figures, shapes, triangles, curves
- To place a 13-foot ramp against the side of a house (#2452)
To place a 13-foot ramp against the side of a house so the ramp rest on a ledge that is 5 feet above the ...
triangles, pythagorean theorem, curves, plane figures, shapes, right triangles, polygons
- Tom and Carol are playing a shadow game (#2604)
Tom and Carol are playing a shadow game. Tom is 6 feet tall and carol is 5 feet tall. If Carol stands at the shadow top of Tom's head, there is two combined shadows total 15 ...
triangles, polygons, shapes, plane figures, curves
- Two satellites are orbiting earth (#250)
Two satellites are orbiting earth. The path of one has the equation x2 +y2 = 2250000. The orbit of the other is 200 km farther fro the centre of earth. In one ...
circle equation, circles, equations, plane figures, shapes, curves
- Two ships leave port at same time (#996)
Two ships leave port at same time. Ship x is heading due north and ship y is heading due east. Twelve hours later they are 600 miles apart. If the ship x had traveled 480 miles from the ...
pythagorean theorem, right triangles, triangles, polygons, shapes, plane figures, curves
- Two triangles are similar (#1169)
Two triangles are similar. One triangle is 4,2,3 the second one is 12,9,6.
Which fraction represents the ratio of the lengths of the sides of the small triangle to the lengths of the large triangle?
Is it 1/3 , 4/9, 1/2...
shapes, polygons, plane figures, triangles, similar triangles, curves
- What is the surface area (#2150)
What is the surface area of a cylinder that is 4 foot radius and 35 feet long?
solid figures, curves, cylinders, area, surface area, circumference, circles, plane figures, shapes
- When you buy a TV (#781)
When you buy a TV, the size refers to the diagonal. You have a cabinet that is 40 inches by 50 inches. You want to buy a 72 inch Plasma High Definition TV to watch the Super ...
triangles, right triangles, polygons, shapes, plane figures, curves
- Wilbur Wrong is flying his remote-control plane (#933)
Wilbur Wrong is flying his remote-control plane in a circle with a radius of 28 meters. His brother, Orville Wrong, clocks the plane at 16 seconds per ...
circumference, circles, plane figures, shapes, curves
