Question

The shadow of a stick of height 1 meter when the angle of elevation of the sun is 60 will be
A.$\dfrac{1}{{\sqrt 3 }}$ meter
B.$\dfrac{1}{3}$ meter
C.$\sqrt 3 $ meter
D.3 meter

Answer 1

Hint: In this question, draw a rough sketch of the situation shown in the question, then use trigonometric formula. As the angle given in the question use $tan\theta=\dfrac{Opposite\, side}{Adjacent\, side}$ to find an answer.

Complete step-by-step answer:
Complete step - by - step solution:-

ACB is a right triangle
where ∠C = 60°
length of AB = height of stick = 1 m
Let AC be the shadow of length x from right angled ΔACB
Or $\sqrt 3 = \dfrac{1}{x}$ since, tan 60° = $\sqrt 3 $
or x = $\dfrac{1}{{\sqrt 3 }}$ meter
Hence, the shadow is of length $\dfrac{1}{{\sqrt 3 }}$ meter .
So, from the above option only A option is correct.


Note: Draw the rough diagram of the question. It is very helpful to solve these types of problems, then carefully use the trigonometric formula. The angle of elevation of an object as seen by the observer is defined as the angle between the horizontal and the line from the object to the observer’s eye. The line in which the observer's eye is there is known as the line of sight.