Question

From a 50-foot-tall Lookout tower, a park ranger sees a fire at an angle of depression of 1.6° how far is the fire from the tower?

Answer 1

`1790.028` feet

Explanation:

Consider a right triangle with a vertical height `50` feet opposite to the angle `\theta=1.6^\circ` & base `b` & use `\tan \theta` as follows

`\tan\theta=\frac{50}{b}`

`\tan1.6^\circ=\frac{50}{b}`

`b=\frac{50}{\tan1.6^\circ}`

`=1790.028\ \text{feet}`

Hence, the distance of fire from tower is `1790.028` feet