Question

A bow hunter is perched in a tree 18 feet off the ground. If the angle of depression from him to his prey is 28 degrees, how far will the arrow have to travel to hit his target?

Answer 1

Solution

- We can make a sketch of the scenario as follows:

- From the above, we can see that a right-angled triangle is formed with the tree height of 18 feet being the Opposite of the triangle, with the angle of depression, 28 degrees, while the distance from the treetop to the target.

- Thus, we can find the value of x using SOHCAHTOA as follows:

$\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \\ \theta=28\degree,Opposite=18,Hypotenuse=x \\ \\ \therefore\sin28\degree=\frac{18}{x} \\ \\ \text{ Make }x\text{ the subject of the formula} \\ x=\frac{18}{\sin28\degree}\approx38.341ft \end{gathered}$

Final Answer

The distance the arrow will travel is 38.341ft