# Right triangle - examples - page 5

1. Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
2. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
3. Hexagon
There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
4. Cube - angles
Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
5. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
6. Climb
On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
7. ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
8. Rotary cone
The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
9. Triangular prism
Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
10. Recursion squares
In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
11. Diagonals of the rhombus
Calculate height of rhombus whose diagonals are 12 cm and 19 cm.
12. Tower
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
13. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
14. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
15. Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
16. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
19. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
20. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.

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