Trigonometry - Height & Distance Questions with Solutions

20 questions7 easy10 medium3 hard

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.

All Questions Easy Medium Hard

Q1.
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 $t an^{- 1} 3$ and $t an^{- 1} 2$ at A and B respectively. The height of the pillar is
A. 10 mB. 8 mC. 12 mD. 15 m
easyAsked in NIMCET 2023View solution ›
Q2.
The angle of elevation of the top of a tower from a point on the ground 30 m away from its foot is $60^{\circ}$ . The height of the tower is
A. $103$ mB. $30$ mC. $303$ mD. $60$ m
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Q3.
A tower stands vertically on level ground. From a point on the ground $30 m$ away from its foot, the angle of elevation of the top of the tower is $60^{\circ}$ . The height of the tower is
A. $103 m$ B. $303 m$ C. $30 m$ D. $153 m$
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Q4.
A ladder leaning against a vertical wall makes an angle of $60^{\circ}$ with the ground. If the foot of the ladder is $4 m$ away from the wall, the length of the ladder is
A. $83 m$ B. $43 m$ C. $8 m$ D. $23 m$
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Q5.
The length of the shadow of a vertical pole is $3$ times its height. The angle of elevation of the sun is
A. $30^{\circ}$ B. $45^{\circ}$ C. $60^{\circ}$ D. $90^{\circ}$
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Q6.
A kite is flying at a height of $60 m$ above the ground. The string attached to it is taut and makes an angle of $60^{\circ}$ with the ground. The length of the string is
A. $403 m$ B. $203 m$ C. $603 m$ D. $120 m$
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Q7.
Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is
A. 273 mB. 173 mC. 200 mD. 300 m
easyAsked in NIMCET 2025View solution ›