The height of the traffic light is 21.788 ft.
Given that Andrew walks exactly 20 feet from the base of the traffic light and looks up to the angle from his eyes to the top of the traffic light is 40°.
As the figure attached below, we can see the right triangle formed from the situation,
From the question,
The distance walked by Andrew from the traffic light, BC = 20 feet
Height of Andrew's eye = 5 feet
We want to find the height of traffic light.
Height of traffic light =height Ab +distance from eye
In the triangle ABC,
tan Θ= Height/Base
tan Θ=AB/BC
tan C= AB/BC
tan 40=AB/20
multiply both sides with 20, we get
20×tan 40=AB
20×0.839=AB
AB=16.78 ft
Now, we will find the height of traffic light, we get
height of the traffic light, H= AB + Height of Andrew's eye
H=16.78+5
H=21.78 ft
Hence, the height of the traffic light when Andrew walks exactly 20 feet from the base of the traffic light and looks up to the angle from his eyes to the top of the traffic light is 40° is 21.78 ft.
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