Question

You are sitting at the edge of the Grand Canyon admiring the view when you notice a tour group at the bottom of the canyon. You estimate that the angle of depression from your spot on the edge to the group is 39°. The sign that says that the bottom of the canyon is 5000 ft below the rim: What is your line of sight distance?

Answer 1

7949.13 feet

Explanation:

We are given that,

Angle of depression from the spot to the group = 39°

Height of Grand Canyon = 5000 feet.

So, we will get the following figure of a right triangle.

As, 'in a right triangle, the angles and the sides can be written in trigonometric form'.

We get,
`\sin A=(perpendicular)/(hypotenuse)`

i.e.
`\sin 39=(5000)/(x)`

i.e.
`x=(5000)/(\sin 39)`

i.e.
`x=(5000)/(0.629)`

i.e. x = 7949.13 feet

Thus, the line of sight distance is 7949.13 feet.