Question

Chewbacca is standing from atop a plateau 500 feet in the air looking down ata Jedi Trainee. If the Jedi Trainee is 150 feet away from the base of theplateau, what is the angle of depression from Chewbacca to the Jedi Trainee ifChewbacca's eye height is 7.25 feet?Show your work here and explain how you arrive at your answer.

Answer 1

In the given situation the angle of depression is θ. To find it, use the trigonometric ratio of tangent of angle θ in a right triangle (the ratio of tangent is the relation between the two legs of a right traingle):

`\tan \theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}}`

In the given situation the opposite leg to the angle of depresion is the distance between the base of the plateau and the Jedi Trainee and the adjacent leg is the sum of 500ft in the air and Chewbacca's eye height:

`\begin{gathered} \tan \theta=(150ft)/(500ft+7.25ft) \\ \\ \tan \theta=(150)/(507.25) \\ \\ \tan ^(-1)(\tan \theta)=\tan ^(-1)((150)/(507.25)) \\ \\ \theta=\tan ^(-1)((150)/(507.25)) \\ \\ \theta\approx16.47 \end{gathered}`

Then, the angle of depression from Chewbacca to the Jedi Trainee is approximately 16.47°