A ladder long leans against a vertical wall so that its foot is from the wall

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

Problem

A ladder 15 m15\,\text{m} long leans against a vertical wall so that its foot is 9 m9\,\text{m} from the wall. The ladder, wall and ground form a right-angled triangle. Let θ\theta be the angle between the ladder and the ground. (i) Calculate the height (in metres) that the ladder reaches on the wall. (ii) Using the dimensions of the triangle, find sin⁡θ\sin \theta, cos⁡θ\cos \theta and tan⁡θ\tan \theta in simplest fractional form. (iii) Determine the value of θ\theta correct to the nearest whole degree.

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