# Pythagorean theorem - examples - page 19

1. Chord circle The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
2. Hypotenuse Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
3. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
4. 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.
5. Body diagonal Find the cube surface if its body diagonal has a size of 6 cm.
6. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
7. 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.
8. The ladder The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
9. 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?
10. 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.
11. 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.
12. 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.
13. Diamond perimeter Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm.
14. 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.
15. 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?
16. Equilateral triangle The equilateral triangle has a 23 cm long side. Calculate its content area.
17. 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?
18. 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?
19. 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.
20. Body diagonal The cuboid has a volume of 32 cm3. 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.