Final answer:
The angle of elevation of the sun, when the shadow's length is \(\sqrt{3}\) times the tree's height, is 30°. This is found using the tangent function, which leads to the calculation that the tangent of the angle is 1/\(\sqrt{3}\), corresponding to a 30° angle. The correct answer is a. 30°.
Step-by-step explanation:
The angle of elevation of the sun, when the length of the shadow of a tree is \(\sqrt{3}\) times the height of the tree, can be determined using trigonometric ratios.
Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.
In this scenario, the height of the tree represents the opposite side, and the length of the tree's shadow represents the adjacent side. Therefore, we can set up the following equation using the tangent of the angle of elevation (\(\theta\)):
\[\tan(\theta) = \frac{height}{shadow} = \frac{1}{\sqrt{3}}\]
To solve for \(\theta\), we find the angle whose tangent is \(\frac{1}{\sqrt{3}}\). This is known to be \(30^\circ\). Therefore, the angle of elevation of the sun is 30°.