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

1. Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
3. 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.
4. Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
5. RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
6. Distance
Wha is the distance between the origin and the point (18; 22)?
7. Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
8. Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
9. Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
10. ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
11. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
12. Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
13. EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
14. Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
15. Semicircle
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
16. 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?
17. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
18. Trapezoid ABCD
Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
19. Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
20. Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?

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