Pythagorean theorem - problems - page 6
Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
- Airplane navigation
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
- EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
If tg α = 0.9, Calculating sin α, cos α, cotg α .
- 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.
- 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.
- Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm2.
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.
- 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?
Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w
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).
- 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!
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
Pythagorean theorem is the base for the right triangle calculator.