 # D.r Black is standing 20 feet from a streetlamp. The lamp is making his shadow 5 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 30°. How tall is the street lamp to the nearest foot? traquealwm 2022-08-06 Answered
D.r Black is standing 20 feet from a streetlamp. The lamp is making his shadow 5 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is ${30}^{\circ }$. How tall is the street lamp to the nearest foot?
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Length of shadow= 5 feet
Distance between him and lamp= 20 feet
Total distance = 25 feet
Angle of elevation = 30 degrees
$\mathrm{tan}30$ = height of lamp/total distance
$\frac{1}{\sqrt{3}}=$height of lamp / 25
$\frac{25}{\sqrt{3}}=$height of lamp
$\frac{25}{1.732}=$ height of lamp
Height of lamp = 14.43 feet.

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