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. For this position it is known that cos⁡θ=45\cos\theta=\dfrac{4}{5}. (i) Find the value of sec⁡θ\sec\theta. (ii) Calculate how high up the wall the ladder reaches. (iii) If the ladder is moved so that the new angle θ′\theta' satisfies sin⁡θ′=sin⁡θ\sin\theta'=\sin\theta, state, with reason, whether sec⁡θ′\sec\theta' will be equal to, greater than or less than the value obtained in part (i).

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