# Pythagorean theorem - problems - page 6

- V-belt

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. - Prism

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? - Arm

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. - Q-Exam

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 mm^{2.} - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - 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. - 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

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 - Elevation

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 v_{a}=5 cm, v_{b}=7 cm and side b is 5 cm shorter than side a. - 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). - 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! - 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.

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Pythagorean theorem is the base for the right triangle calculator.