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Question 7 of 20 · Trigonometry - Height & Distance
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A ladder leaning against a vertical wall makes an angle of with the ground. If the foot of the ladder is away from the wall, the length of the ladder is

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Answer: Option C —

Detailed Solution

figure

1

The ladder is the hypotenuse ; the 4 m gap is the side adjacent to the angle, so use cos.

2

3

⚠ Common trap

(B) m is the height reached on the wall, not the ladder's length.

Quick tip

Hypotenuse

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  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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