The height of an outdoor basketball backboard is $12 \frac { 1 } { 4 }$ feet,and the backboard casts a shadow $17 \frac { 1 } { 2 }$ feet long. Find the angle of elevation of the sun.Round your answer to one decimal place.
?
A)36.0º
B)37.0º
C)35.0º
D)39.0º
E)38.0º

Question

Quizplus · Accepted Answer

We can use the tangent function to solve this problem. Let x be the angle of elevation of the sun. Then, we have:

tan(x) = opposite/adjacent = height of backboard/shadow length
tan(x) = 11/11
x = tan^(-1)(11/11)
x ≈ 45º

However, we need to subtract this angle from 90º to get the angle of elevation of the sun, since the sun's rays are perpendicular to the ground. Thus, we have:

angle of elevation of sun = 90º - 45º = 45º

Therefore, the correct answer is:

C) 35.0º.

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The Height of an Outdoor Basketball Backboard Is $12 \frac { 1 } { 4 }$