# Right triangle - examples - page 24

1. Rectangle 35 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
2. Road drop On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
3. Medians of isosceles triangle The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
4. Two aircraft From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour.
5. Stairway Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
6. A mast A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
7. Rhombus MATH Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120°
8. Plane II A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point
9. Rectangular triangle PQR In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
10. Double ladder The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
11. Diagonals Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
12. Find the area Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
13. Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
14. Equilateral triangle ABC In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
15. Resultant force Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
16. Ladder The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
17. Chord It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
18. Forces on earth directions A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
19. Hexagon area The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
20. Ratio iso triangle The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.

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