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 at it. The angle from his eyes to the top of the traffic light is 40∘. Andrew's eyes are at a height of 5 feet when he looks up. How tall is the traffic light? sin40∘≈0.643 cos40∘≈0.766 tan40∘≈0.839 A triangle matching the description of the text. © 2019 StrongMind. Created using GeoGebra. The traffic light is approximately _[blank]_ feet tall.

Answer 1

Question

Andrew wants to measure the height of a traffic light.He walks exactly 20 feet from the base of the traffic light and look up at it. The angle from his eye to the top of the traffic light is 40□. Andrew

Given

• The height of the traffic light is 21.8 dear
• right angle is formed in this situation

Required to Find

height of the traffic light

Solution

The hieght of The traffic light is 21.8 feet

As shown in the 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 if Andrew's eye = 5 feet

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

from the properties of triangle

$\implies \sf\tan = \frac{height}{base}$

$\implies \sf\tan C = \frac{AB}{BC}$

$\implies \sf \: AB = \tan \: C \times BC$

$\implies \sf \: AB = \tan40 \times 20$

$\implies \sf \: AB = 16.8$

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

More

• right angle is an angle of exactly 90°
• corresponding to a quarter turn
• the side opposite angle 90° is a hypotenuse

a right angle triangle conceals the hypotenuse which meets at 90° angle and the hypotenuse is the longest side of the right angle triangle and is the side opposite the right .