Question

A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?​

Answer 1

`103.78\:\mathrm{ft}`

Explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

`\tan 34^(\circ)=(70)/(x)`, where
`x` is the distance between the base of the tower and the fire.

Solving, we get:

`x=(70)/(\tan 34^(\circ))=103.779267796\approx \boxed{103.78\:\mathrm{ft}}`