Question

If the angle of elevation of temple is \[{60^ \circ }\]then ratio of height of temple with its shadow is
A) \[1:1\]
B) \[1:\sqrt 3 \]
C) \[\sqrt 3 :1\]
D) \[1:2\]

Answer 1

Hint: Here first we have to let the height of the temple to be x and the length of the shadow to be y and then calculate the value of \[\tan \theta \] to get the desired ratio.
\[\tan \theta = \dfrac{{{\text{Perpendicular}}}}{{{\text{base}}}}\]

Complete step-by-step answer:

Let the height of the temple be \[{\text{AB = x}}\]
Let the length of the shadow be \[{\text{BC = y}}\]
Then we have to find the ratio of height of the temple to the length of the shadow.
i.e, we have to find \[\dfrac{x}{y}\]
Also we are given the \[\angle {\text{ACB = }}{60^ \circ }\]
In order to find the ratio of x and y we need to find the value of \[\tan \theta \] where \[\theta = {60^ \circ }\]
We know that \[\tan \theta = \dfrac{{{\text{Perpendicular}}}}{{{\text{base}}}}\]
\[\tan {60^ \circ } = \dfrac{x}{y}\]
Now since we know that \[\tan {60^ \circ } = \sqrt 3 \]
Putting the value we get:
\[\dfrac{x}{y} = \sqrt 3 \]
Therefore,\[x:y = \sqrt 3 :1\]

Hence the ratio of height of the temple to the length of the shadow is \[\sqrt 3 :1\].
Therefore option C is correct.

Note :
The tangent of any angle is equal to the ratio of perpendicular of the right triangle to its base.
  \[\tan \theta = \dfrac{{{\text{Perpendicular}}}}{{{\text{base}}}}\]
Also, \[\tan {60^ \circ } = \sqrt 3 \]