Question

A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of $60^o$ with the level of the ground. Determine 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 tangent function is the ratio of the opposite side and the adjacent side.

Complete step-by-step answer:

Let the wall DC be of the length h. The base of the ladder E is at a distance of 2 m from C as shown, where DE is the ladder. We will apply trigonometric formulas in triangle DCE as follows-

$

  In\;\vartriangle DCE,\; \\

  \tan {60^{\text{o}}} = \dfrac{{CD}}{{CE}} \\

  \sqrt 3 = \dfrac{{\text{h}}}{2} \\

  {\text{h}} = 2\sqrt 3 \;{\text{m}} \\

$


Therefore the height of the wall is 2 x 1.732 = 3.464 m.


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.