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

Answer:

$103.78\:\mathrm{ft}$

Step-by-step 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:

$\tan 34^{\circ}=\frac{70}{x}$, where $x$ is the distance between the base of the tower and the fire.

Solving, we get:

$x=\frac{70}{\tan 34^{\circ}}=103.779267796\approx \boxed{103.78\:\mathrm{ft}}$