Question

Gary spots a monkey as he is looking down at a 69° angle from the top of the Sears Tower, which is 442 m tall. How far away from the tower is the monkey? Round to the nearest hundredth.

Answer 1

The question describes a right triangle with one of the angles as 69 degrees and the side adjacent to the angle 69 degrees is of length 442 m. We are to find the length of the side opposite the angle 69 degrees. Let the distance of the monkey from the tower be x.

Recall that:
`tan(\theta)=\cfrac{opp}{hyp}`

Thus,

`tan(69^o)=\cfrac{x}{442}\\ \\ \Rightarrow x=442tan(69^o)=1,151.45`