Question

A skier is on the top of a 350 meter tall mountain looking down at a tree. The direct path from the tree to the skier is 505 meters. What is the angle of depression from where the skier is standing to the base of the tree

Answer 1

Answer:

$43.87^{\circ}$

Step-by-step explanation:

We are given that

Height of mountain=350 m

Distance  from the tree to the skier=505 m

We have to find the angle of depression from where the skier is standing to the base of the tree.

In triangle ABC

$\frac{AB}{AC}=sin\theta$

By using the formula

$\frac{Perpendicular\;side}{Hypotenuse}=sin\theta$

$\frac{350}{505}=sin\theta$

$sin^{-1}(\frac{350}{505})=\theta$

$\theta=43.87^{\circ}$

Hence, the angle of depression from where the skier is standing to the base of the tree=$43.87^{\circ}$