Question

Andrew wants to measure the height of a traffic light. He walks exactly 20 feet from the base of the traffic light and looks up. The angle from his eyes to the top of the traffic light is 40 degrees. Andrews eyes are at a height of 5 feet when hes looking up . How tall is the traffic light?

The traffic light is approximatly _ feet tall

Answer 1

The height of the traffic light is 21.8 feet.

Solution-

As shown in figure, we can see the right triangle formed from the situation,

From the question,

BC = the distance walked by Andrew from the traffic light = 20 feet

Height of Andrew's eye = 5 feet

Height of the traffic light = AB + Height of Andrew's eye

From the properties of triangle,

`\Rightarrow \tan \theta =(Height)/(Base)`

`\Rightarrow \tan C =(AB)/(BC)`

`\Rightarrow AB=\tan C* BC`

`\Rightarrow AB=\tan 40* 20`

`\Rightarrow AB=16.8`

Therefore, height of the traffic light = AB + Height of Andrew's eye = 16.8+5 = 21.8 feet