Right triangle - examples - page 8
- 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.
- 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.
- 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.
- EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
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.
- XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
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?
- 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.
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
- Sphere and cone
Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
Average climb of the road is given by ratio 1:15. By what angle road average climb?
- 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!
- Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
- 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.
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).
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
- Triangular prism
The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
See also our right triangle calculator.