# Pythagorean theorem - math word problems

1. Rhombus
Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm.
2. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
3. Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
4. Without Euclid laws
Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
5. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
6. Goniometric form
Determine goniometric form of a complex number ?.
7. Diagonals
Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
8. Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
9. Canopy
Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
10. Cone
Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
11. Diagonal
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
12. Arm
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
13. Surveyor
Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?
14. Base
Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm.
15. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
16. Bridge
The bridge arc has a span 34 m and height 3 m. Calculate the radius of the circle arc of this bridge.
Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
18. Arc
Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
19. RT and circles
Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
20. Square2
Side of the square is a = 6.2 cm, how long is its diagonal?

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Pythagorean theorem is the base for the right triangle calculator.