# Right triangle - examples - page 8

1. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
2. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
3. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
4. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
5. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
6. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
7. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
8. Euklid4 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
9. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
10. Slope of the pool Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
11. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
12. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
13. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
14. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
15. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
16. Road Average climb of the road is given by ratio 1:15. By what angle road average climb?
17. Elevation What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
18. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
19. Euclid2 In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
20. Sea How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).

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