Question

A park ranger is looking out from their station at a 30 degree angle , angle of depression. The ranger is 80 feet above the ground.how far is it from the ranger up in the station down the fire?

Answer 1

Answer:

$\boxed{\text{160 ft}}$

Step-by-step explanation:

The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).

The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC  of the right triangle ABC.

sin 30 = 80/AC

AC  = 80/sin30 = 80/0.5 = 160 ft

The distance is $\boxed{\textbf{160 ft}}$