The angle of elevation of the sun when the length of the shadow of pole is $\sqrt 3 $
times the height of the pole is
\[
(A){\text{ 3}}{{\text{0}}^0} \\
(B){\text{ 4}}{{\text{5}}^0} \\
(C){\text{ 6}}{{\text{0}}^0} \\
(D){\text{ 1}}{{\text{5}}^0} \\
\]
Answer
384.9k+ views
Hint: Draw figure and then use trigonometry identity $\cot \theta = \dfrac{{Base}}{{Perpendicular}}$.
Let AB be the height of the pole and BC be its shadow.
As, we are given the ratio of the length of the pole and its shadow.
Let the height of the pole be AB$ = h$ units.
So, the length of its shadow will be BC $ = \sqrt 3 h$ units.
So, we must find an angle of elevation.
Now, we can only use the given condition.
So, the best way to find the angle of elevation using trigonometric formulas.
So, solving using given conditions.
Let, $\angle ACB = \theta $.
And , \[\theta \] will be the angle of elevation of sun
And we know that $\cot \theta = \dfrac{{Base}}{{Perpendicular}}$.
Here, the base will be BC.
And, perpendicular will be AB.
So, here putting the value of base and perpendicular in $\cot \theta $ we will get.
$\cot \theta = \dfrac{{BC}}{{AB}} = \dfrac{{\sqrt 3 h}}{h} = \sqrt 3 $
So, from the above equation we can write,
\[\theta = {\cot ^{ - 1}}\left( {\sqrt 3 } \right)\] (1)
Using inverse trigonometric formulas. We can say that $\theta = {30^0}$
Hence, the angle of elevation of the sun will be ${30^0}$.
Hence, the correct Option will be A.
Note: Whenever we come up with these types of problems, first we should draw the figure according to the given conditions in question, then we will use the trigonometric functions to get the angle of elevation which will be the easiest and efficient method. And we should remember that object and its shadow are always perpendicular to each other.

Let AB be the height of the pole and BC be its shadow.
As, we are given the ratio of the length of the pole and its shadow.
Let the height of the pole be AB$ = h$ units.
So, the length of its shadow will be BC $ = \sqrt 3 h$ units.
So, we must find an angle of elevation.
Now, we can only use the given condition.
So, the best way to find the angle of elevation using trigonometric formulas.
So, solving using given conditions.
Let, $\angle ACB = \theta $.
And , \[\theta \] will be the angle of elevation of sun
And we know that $\cot \theta = \dfrac{{Base}}{{Perpendicular}}$.
Here, the base will be BC.
And, perpendicular will be AB.
So, here putting the value of base and perpendicular in $\cot \theta $ we will get.
$\cot \theta = \dfrac{{BC}}{{AB}} = \dfrac{{\sqrt 3 h}}{h} = \sqrt 3 $
So, from the above equation we can write,
\[\theta = {\cot ^{ - 1}}\left( {\sqrt 3 } \right)\] (1)
Using inverse trigonometric formulas. We can say that $\theta = {30^0}$
Hence, the angle of elevation of the sun will be ${30^0}$.
Hence, the correct Option will be A.
Note: Whenever we come up with these types of problems, first we should draw the figure according to the given conditions in question, then we will use the trigonometric functions to get the angle of elevation which will be the easiest and efficient method. And we should remember that object and its shadow are always perpendicular to each other.
Recently Updated Pages
Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the nlx method How is it useful class 11 chemistry CBSE

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Why do we use cooking utensils made up of copper class 11 physics CBSE

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE

State the laws of reflection of light

Explain zero factorial class 11 maths CBSE
