# Pythagorean theorem - examples - page 18

1. Forces Determine the resultant of two perpendicular forces F1 = 560 N and second force of 25% smaller.
2. Umbrella Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.
3. Circumscribed circle to square Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square.
4. Billboard Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard.
5. Points on circle In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are i
6. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
7. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
8. 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?
9. Square Calculate the side of a square with a diagonal measurement 10 cm.
10. Flowerbed Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of the
11. Trio 2 Decide whether trio of numbers is the side of a right triangle: 26,24,10.
12. Add vector Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
13. 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.
14. Four ropes TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
15. Cableway Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
16. Isosceles trapezoid Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
17. Diagonals of diamond Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
18. Is right triangle Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
19. Land - isosceles trapezoid Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
20. Church roof 2 The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?

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Pythagorean theorem is the base for the right triangle calculator.