Question

If the height of a vertical pole is $\sqrt 3 $ times the length of its shadow on the ground, then the angle of elevation of the sun is,
A. $30^o$
B. $60^o$
C. $45^o$
D. $75^o$

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 the vertical pole be the line segment CD and the shadow be CE. We have been given that the height of the pole is $\sqrt 3 $ times the length of the shadow.

Let the length of the shadow be h, then the height of the pole will be $\sqrt 3 $h.

From the figure it is clear that the angle of elevation of the sun will be the angle of the line ED from the ground level. We will apply trigonometric formulas in triangle DCE.

In $\vartriangle$ DCE, 

$tanE = \dfrac{{perpendicular}}{{base}}$

$tanE = \dfrac{{CD}}{{CE}} $

$tanE = \dfrac{{\sqrt 3 {\text{h}}}}{{\text{h}}} $

$tanE = \sqrt 3 = \tan {60^{\text{o}}} $

$\angle {\text{E}} = {60^{\text{o}}} $

This is the angle of elevation of the sun. The correct answer is B. $60^o$.

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.