Question

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

Answer 1

Hint: The angle of elevation is the angle above the eye level of the observer towards a given point. The angle of depression is the angle below the eye level of the observer towards a given point. The cosine function is the ratio of the adjacent side and the hypotenuse.

Complete step-by-step answer:

Let DE be the ladder of length 15 m. It is given that the ladder makes an angle $60^o$ with the vertical wall CD. We have to find the height of the wall CD. We will apply trigonometric formulas in triangle DCE.

$

  In\;\vartriangle DCE, \\

  \cos {60^{\text{o}}} = \dfrac{{CD}}{{DE}} \\

  \dfrac{1}{2} = \dfrac{{CD}}{{15}} \\

  CD = \dfrac{{15}}{2}\;{\text{m}} \\

$

This is the height of the wall.


Note: In such types of questions, it is important to read the language of the question carefully and draw the diagram step by step correctly. When the diagram is drawn, we just have to apply basic trigonometry to find the required answer.