# Pythagorean theorem - examples - page 19

- Hypotenuse

Calculate the length of the hypotenuse of a right triangle with a cathetuses 71 cm and 49 cm long. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Axial cut

The cone surface is 388.84 cm^{2}, the axial cut is an equilateral triangle. Find the cone volume. - Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter. - The ladder

The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall? - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Kite

John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending. - Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle. - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Diamond perimeter

Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm. - The ditch

Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch? - Circular ring

Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form. - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Square

Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg? - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder? - Pyramid

The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid. - Central park in city

The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path. - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

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Pythagorean theorem is the base for the right triangle calculator.