# Right triangle - math word problems

1. Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
2. Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
3. Minute
Two boys started from one place. First went north at velocity 3 m/s and the second to the east with velocity 4 m/s. How far apart they are after minute?
4. The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
5. Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
6. Rhumbline
Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
7. Horizontal Cylindrical Segment
How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
8. Broken tree
The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
9. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
10. A mast
A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
11. Rectangular triangle PQR
In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
12. Circle tangent
It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
13. Triangular prism
The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
14. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
15. Church roof
The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
16. Pyramid in cube
In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
17. Pyramid four sides
In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
18. RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
19. The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
20. Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.

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