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Question 9 of 20 · Trigonometry - Height & Distance
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From the top of a lighthouse high, the angles of depression of two ships on the same side of it, in a straight line with its foot, are and . The distance between the two ships is

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Answer: Option D —

Detailed Solution

figure

1

An angle of depression from the top equals the angle of elevation at the ship (alternate angles).

2

Nearer ship ( ):

3

Farther ship ( ):

4

Distance

⚠ Common trap

(B) adds the two distances, which is correct only when the ships are on opposite sides of the lighthouse.

Quick tip

Same side: with ; opposite sides:

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More Trigonometry - Height & Distance Questions

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  1. Q1.From the top of a viewpoint at a height of 80 m, the angles of depression of the top and bottom of a flag standing on the same plane are and . Find the height of the flag.
  2. Q2.A line segment AB of length 10 m passes through the foot of a vertical pillar, the foot lying between A and B. The top of the pillar subtends angles and at A and B respectively. The height of the pillar is
  3. Q3.A man observes the angle of elevation of the top of a mountain to be . He walks 1000 feet nearer and finds the angle of elevation to be . What is the distance of the first point of observation from the foot of the mountain?
  4. Q4.A person standing at a point due south of a tower observes its angle of elevation as . He walks due west to a point , where the angle of elevation is . At a point on produced, the angle of elevation is . Then is equal to
  5. Q5.The angle of elevation of the top of a tower from a point on the ground 30 m away from its foot is . The height of the tower is

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Trigonometry - Height & Distance — Preparation

This question tests your understanding of Trigonometry - Height & Distance, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

Height and distance questions apply trigonometry to real-world situations, such as finding the height of a tower, the width of a river, or the distance between two ships. The two key ideas are the angle of elevation (looking up at an object) and the angle of depression (looking down at an object), both measured from the horizontal. Most questions are solved using tan theta = opposite/adjacent in one or two right triangles. Common types include an observer moving towards a tower, angles from the top and bottom of a building, and objects seen from a height. Drawing a clear diagram and knowing the values at 30, 45 and 60 degrees (tan 30 = 1/sqrt 3, tan 45 = 1, tan 60 = sqrt 3) solves the vast majority of questions. Practise the height and distance questions below, each with a diagram-based step-by-step solution.

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