Height and Distance Mcqs

The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?

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The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?

A. 5 metres
B. 8 metres
C. 10 metres
D. 12 metres

From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is :_________?

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From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is :_________?

A. 149 m
B. 156 m
C. 173 m
D. 200 m
Let AB be the tower. Then, ∠APB = 30° and AB = 100 m, AB/AP = tan 30° = 1/√3 AP = (AB X √3)= 100√3 m. = (100 X 1.73) m = 173 m.

If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.

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If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.

A. 50°
B. 60°
C. 70°
D. 80°
Let AB be the pole and AC be its shadow. Let angle of elevation, ∠ACB = θ. Then, AB = 2√3m, AC = 2 m. tan θ = AB/AC = 2√3/2 = √3 θ = 60°. So,the angle of elevation is 60°

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is :_________?

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Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is :_________?

A. 173 m
B. 200 m
C. 273 m
D. 300 m
Let AB be the lighthouse and C and D be the
positions of the ships. Then,
AB = 100 m, ∠ACB = 300 and ∠ADB = 45°.
AB/AC = tan 30° = 1/√3
AC = AB X √3 = 100√3 m.
AB/AD = tan 45° = 1 ⇒ AD = AB = 100 m.
CD = (AC + AD) = (100√3 + 100) m
= 100 (√3 +1) m = (100 X 2.73) m = 273 m.

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is :_________?

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The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is :_________?

A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m
Let AB be the wall and BC be the ladder. Then, ∠ACB = 60° and AC = 4.6 m. AC/BC = Cos 60° = 1/2 BC = 2 X AC = (2 X 4.6) m = 9.2 m.