After substituting, the h terms cancel out, leaving tan θ = (1)/(√3). We know that the angle whose tangent is (1)/(√3) is 30^°. Therefore, the angle of elevation of the Sun is 30^°.

If the length of the shadow on the ground of a pole is $\sqrt{3}$ times the height of the pole, then the angle of elevation of the Sun is :

Answer: The angle of elevation of the Sun is $30^\circ$ .

Step-by-step solution

Step 1: Define variables and set up the problem

Let $h$ represent the height of the pole and $s$ represent the length of its shadow on the ground. According to the problem statement, the length of the shadow is $\sqrt{3}$ times the height of the pole, which can be written as $s = \sqrt{3}h$ .

Step 2: Formulate the trigonometric relationship

The pole, its shadow, and the line of sight from the top of the pole to the end of the shadow form a right-angled triangle. The angle of elevation, $\theta$ , is the angle between the ground (shadow) and the line of sight. In this triangle, the height of the pole ( $h$ ) is the side opposite to $\theta$ , and the length of the shadow ( $s$ ) is the side adjacent to $\theta$ . Therefore, we can use the tangent function.

Step 3: Substitute the given relationship into the tangent equation

Now, substitute the given relationship $s = \sqrt{3}h$ into the tangent equation. This will allow us to simplify the expression and find the value of $\tan \theta$ .

Step 4: Simplify and find the angle of elevation

After substituting, the $h$ terms cancel out, leaving $\tan \theta = \frac{1}{\sqrt{3}}$ . We know that the angle whose tangent is $\frac{1}{\sqrt{3}}$ is $30^\circ$ . Therefore, the angle of elevation of the Sun is $30^\circ$ .

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If the length of the shadow on the ground of a pole is 3\sqrt{3}3​ times the height of the pole, then the angle of elevation of the Sun is :