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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?

Respuesta :

Answer:

7949.13 feet

Step-by-step 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, [tex]\sin A=\frac{perpendicular}{hypotenuse}[/tex]

i.e. [tex]\sin 39=\frac{5000}{x}[/tex]

i.e. [tex]x=\frac{5000}{\sin 39}[/tex]

i.e. [tex]x=\frac{5000}{0.629}[/tex]

i.e. x = 7949.13 feet

Thus, the line of sight distance is 7949.13 feet.

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