# Right triangle - 9th grade (14y) - math problems

1. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5). The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
3. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
5. A box A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
6. Hypotenuse - RT A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
7. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area. The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
9. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
10. A boy A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
11. Diamond diagonals Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
12. Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
13. Cube cut The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
14. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
15. Roof cover Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m2 of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
16. A bridge A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
17. Equilateral triangle Calculate the area of an equilateral triangle with circumference 72cm.
18. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
19. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
20. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.

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