# Right triangle - math word problems

1. Balloon and bridge
From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
2. Diagonals at right angle
In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
4. An angle
An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
5. Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
6. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
7. Rectangular field
A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
8. Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor an
9. Children playground
The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
11. Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
12. Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
13. Cuboidal room
Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
14. Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
15. Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
16. Circle described
The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
17. Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
18. Octagonal tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
19. Land
Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
20. Find diagonal
Find diagonal of cuboid with length=20m width=25m height=150m

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