# Triangle - 9th grade (14y) - examples - page 6

1. Circumscribing
Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
2. Triangular prism
Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
3. Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
4. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
5. Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
6. Circumferential angle
Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:3:10. Determine the size of the angles of the triangle ΔABC.
7. Horizon
The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
8. Boat
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
9. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
10. Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
11. Aircraft
The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
12. Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
13. Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
14. 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.
15. Map - climb
On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track?
16. Height
Calculate height of the equilateral triangle if its perimeter is 8?
17. 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?
18. 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.
19. Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
20. Railway
Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?

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