A ladder long rests against a vertical wall

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

A ladder 10 m10\,\text{m} long rests against a vertical wall. The foot of the ladder is on level ground and makes an acute angle θ\theta with the ground such that tan⁡θ=34\tan\theta = \dfrac{3}{4}. (i) Determine sin⁡θ\sin\theta and cos⁡θ\cos\theta. (ii) Find the height of the top of the ladder above the ground. (iii) Find the horizontal distance of the foot of the ladder from the wall. (iv) Verify that your answers for parts (ii) and (iii) satisfy the Pythagorean theorem for the triangle formed by the ladder, the wall and the ground.

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