Right-Angled Triangle (Copy)
1.
In a right triangle, one acute angle is 30°, hypotenuse 10 cm.
Find the side opposite the 30° angle.
2.
In a right triangle, an angle is 60°, adjacent side = 5 cm.
Find the hypotenuse.
3.
A right triangle has hypotenuse 13 cm and one leg 5 cm.
Find the angle opposite the leg of length 5 cm.
4.
A ladder leans against a wall making an angle of 70° with the ground. The ladder is 8 m long.
Find the height reached on the wall.
5.
A kite string is 40 m long and makes an angle of 55° with the ground.
Find the height of the kite above the ground.
6.
A building is 30 m tall. A person stands 20 m away.
Find the angle of elevation of the top of the building.
7.
A ship sails 10 km due east and then 6 km due north.
Find the bearing of the ship from the starting point.
8.
A hill has a slope making an angle of 25° with the horizontal. The slope length is 120 m.
Find the vertical height of the hill.
9.
A flagpole casts a shadow of length 18 m. The angle of elevation of the sun is 42°.
Find the height of the flagpole.
10.
From the top of a building 50 m tall, the angle of depression to a car on the ground is 35°.
Find the horizontal distance of the car from the building.
11.
A plane climbs at an angle of 12° to the horizontal. After flying 5 km along this path, how high is the plane above the ground?
12.
A ladder 10 m long leans against a wall. It reaches 8 m high.
Find the angle between the ladder and the ground.
13.
In a right triangle, side opposite θ = 7, hypotenuse = 25.
Find θ.
14.
A tree casts a shadow 15 m long. If the tree is 9 m tall, find the angle of elevation of the sun.
15.
From the top of a 40 m lighthouse, the angle of depression to a boat is 20°.
Find the distance of the boat from the foot of the lighthouse.
16.
A guy wire is attached to the top of a vertical pole 12 m high. If the wire makes 60° with the ground, find the length of the wire.
17.
From a point 25 m away from a building, the angle of elevation to the top is 48°.
Find the height of the building.
18.
In a right triangle, adjacent = 9, opposite = 12.
Find the acute angle.
19.
A ramp rises 1.2 m over a horizontal distance of 3.6 m.
Find the angle of inclination of the ramp.
20.
From the top of a tower, the angle of depression to a point on the ground is 28°. If the tower is 60 m tall, find the horizontal distance.
21.
In a right triangle, angle = 37°, hypotenuse = 15 cm.
Find the adjacent side.
22.
A boat sails 5 km east then 12 km south.
Find the bearing of the boat from the starting point.
23.
A vertical mast 18 m high is supported by a wire anchored 12 m from the base.
Find the angle the wire makes with the ground.
24.
From a point on the ground, the angle of elevation of the top of a cliff is 72°. If the cliff is 150 m tall, find the horizontal distance from the point to the foot of the cliff.
25.
In a right triangle, angle = 65°, adjacent side = 11 cm.
Find the opposite side.
26.
A ladder 7 m long rests against a wall at angle 68° with the ground.
Find the height reached.
27.
A plane is flying at a height of 2 km. A point on the ground is 5 km horizontally from the plane.
Find the angle of elevation of the plane.
28.
A ramp is built with a length of 4 m making 20° with the horizontal.
Find its vertical height.
29.
From a ship at sea, the angle of elevation of the top of a lighthouse is 16°. If the lighthouse is 45 m tall, find the distance of the ship from its base.
30.
A road goes up a hill at an inclination of 7°. If the horizontal length of the road is 300 m, find the vertical rise.
1.
Opp = hyp × sin30° = 10 × 0.5 = 5 cm.
2.
Hyp = adj ÷ cos60° = 5 ÷ 0.5 = 10 cm.
3.
sinθ = opp/hyp = 5/13 ≈ 0.3846.
θ = sin⁻¹(0.3846) ≈ 22.6°.
4.
Height = hyp × sin70° = 8 × 0.9397 ≈ 7.5 m.
5.
Height = 40 × sin55° ≈ 40 × 0.8192 ≈ 32.8 m.
6.
tanθ = opp/adj = 30/20 = 1.5.
θ = tan⁻¹(1.5) ≈ 56.3°.
7.
Bearing = tan⁻¹(6/10) = tan⁻¹(0.6) = 31° north of east.
So bearing = 059°.
8.
Height = 120 × sin25° ≈ 120 × 0.4226 ≈ 50.7 m.
9.
Height = 18 × tan42° ≈ 18 × 0.9004 ≈ 16.2 m.
10.
Distance = 50 ÷ tan35° ≈ 50 ÷ 0.7002 ≈ 71.4 m.
11.
Height = 5 × sin12° ≈ 5 × 0.2079 ≈ 1.0 km.
12.
sinθ = opp/hyp = 8/10 = 0.8.
θ = sin⁻¹(0.8) ≈ 53.1°.
13.
θ = sin⁻¹(7/25) = sin⁻¹(0.28) ≈ 16.3°.
14.
tanθ = 9/15 = 0.6.
θ = tan⁻¹(0.6) ≈ 31.0°.
15.
Distance = 40 ÷ tan20° ≈ 40 ÷ 0.3640 ≈ 110.0 m.
16.
Wire = 12 ÷ sin60° = 12 ÷ 0.866 ≈ 13.9 m.
17.
Height = 25 × tan48° ≈ 25 × 1.1106 ≈ 27.8 m.
18.
tanθ = 12/9 = 1.333.
θ = tan⁻¹(1.333) ≈ 53.1°.
19.
tanθ = 1.2/3.6 = 0.333.
θ = tan⁻¹(0.333) ≈ 18.4°.
20.
Distance = 60 ÷ tan28° ≈ 60 ÷ 0.5317 ≈ 112.9 m.
21.
Adjacent = hyp × cos37° = 15 × 0.7986 ≈ 12.0 cm.
22.
Bearing = tan⁻¹(12/5) ≈ tan⁻¹(2.4) = 67.4° south of east.
Bearing = 090°+67.4° = 157°.
23.
θ = tan⁻¹(18/12) = tan⁻¹(1.5) ≈ 56.3°.
24.
Distance = 150 ÷ tan72° ≈ 150 ÷ 3.0777 ≈ 48.7 m.
25.
Opp = 11 × tan65° ≈ 11 × 2.1445 ≈ 23.6 cm.
26.
Height = 7 × sin68° ≈ 7 × 0.9272 ≈ 6.5 m.
27.
θ = tan⁻¹(2/5) = tan⁻¹(0.4) ≈ 21.8°.
28.
Height = 4 × sin20° ≈ 4 × 0.3420 ≈ 1.37 m.
29.
Distance = 45 ÷ tan16° ≈ 45 ÷ 0.2867 ≈ 157.0 m.
30.
Rise = 300 × tan7° ≈ 300 × 0.1228 ≈ 36.8 m.