# Pythagorean theorem - problems - page 6

1. Height
Is right that in any right triangle height is less or equal half of the hypotenuse?
2. Right triangle
Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
3. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
4. Track arc
Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
5. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
6. V-belt
Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
7. Prism
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
8. Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
10. Arm
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
11. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
12. Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
13. EQL triangle
14. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
15. Q-Exam
If tg α = 0.9, Calculating sin α, cos α, cotg α .
16. Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm2.
17. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
18. Euklid4
Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
19. Sphere and cone
Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
20. Pit
Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w

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Pythagorean theorem is the base for the right triangle calculator.