# Right triangle - 9th grade (14y) - examples - page 9

1. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
2. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
3. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
4. Railway Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
5. Column Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
6. Circle On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
7. Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
8. Diagonals Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
9. Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
10. 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.
11. Prism - box The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
12. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
13. Above Earth To what height must a boy be raised above the earth in order to see one-fifth of its surface.
14. The cone The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
15. Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
16. Vertical prism The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
17. Common chord Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
18. Leg Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
19. Chord AB What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
20. Isosceles trapezoid The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.

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