# Pythagorean theorem - math word problems

1. Two diagonals The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
2. Resultant force Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
3. Hypotenuse Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
4. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
5. Diagonals Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
6. Cuboid easy The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
7. Chocolate roll The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
8. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
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. Plane II A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point
11. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
12. Wall diagonal Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
13. Square s3 Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
14. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
15. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
16. Diagonals A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal. 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.
18. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
19. Circle - AG Find the coordinates of circle and its diameter if its equation is: ?
20. Equation of circle find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.

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Pythagorean theorem is the base for the right triangle calculator.