Pythagorean theorem - problems - page 6
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
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)?
- 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.
- Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm2.
- 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.
- 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.
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.
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
- 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
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).
- 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.
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.
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
- 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!
- Glass mosaic
How many dm2 glass is nessesary to produc 39 slides of a regular 6-gon, whose side has length 23 cm? Assume that cutting glass waste is 12%.
Pythagorean theorem is the base for the right triangle calculator.