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Some Applications of Trigonometry · Class 10 · CBSE Mathematics

A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60^circ with the wall, find the height of the wall.

Practice question from Some Applications of Trigonometry (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · Subjective · Q-D89829

A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60∘60^\circ with the wall, find the height of the wall.

Answer: Let the height of the wall be hh meters. Since the ladder makes an angle of 60∘60^\circ with the wall, the angle it makes with the ground is 90∘−60∘=30∘90^\circ - 60^\circ = 30^\circ. Alternatively, using the triangle formed by the wall, ladder, and ground, cos⁡(60∘)=height of the walllength of the ladder=h15\cos(60^\circ) = \frac{\text{height of the wall}}{\text{length of the ladder}} = \frac{h}{15}. Since cos⁡(60∘)=12\cos(60^\circ) = \frac{1}{2}, we have h=15×12=7.5h = 15 \times \frac{1}{2} = 7.5 meters.

Solution

Using the cosine ratio in the right-angled triangle, cos⁡(60∘)=h15\cos(60^\circ) = \frac{h}{15}, which gives h=15×12=7.5 mh = 15 \times \frac{1}{2} = 7.5\text{ m}.

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