A ladder long rests against a vertical wall and makes an acute angle with the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

A ladder 10 m10\,\text{m} long rests against a vertical wall and makes an acute angle θ\theta with the horizontal ground. Initially, the top of the ladder is 5013 m\dfrac{50}{13}\,\text{m} above the ground. (i) Show that sin⁡θ=513\sin\theta = \dfrac{5}{13} for the initial position. (ii) Find cos⁡θ\cos\theta and hence calculate the horizontal distance of the foot of the ladder from the wall. (iii) The foot of the ladder is now moved directly away from the wall until sin⁡θ\sin\theta becomes 35\dfrac{3}{5} while the ladder length remains the same. Determine the new horizontal distance of the foot from the wall. (iv) Calculate by how much the foot of the ladder has been moved and comment on whether the ladder is now steeper or less steep than before.

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