The height of an outdoor basketball backboard is feet, and the backboard casts a shadow 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

The height of an outdoor basketball backboard is  feet, and the backboard casts a shadow  feet long. Find the angle of elevation of the sun.Round your answer to one decimal place.
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A)36.0º 
B)37.0º 
C)35.0º 
D)39.0º 
E)38.0º

Quizplus · Accepted Answer

The angle of elevation can be found using the tangent function:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the backboard (11 feet) and the adjacent side is the length of the shadow (11 feet).

tan(angle) = 11/11

Simplifying,

tan(angle) = 1

Using a calculator, we can find the angle whose tangent is 1:

angle = 45º

However, this is the angle of elevation of the sun at noon, when there is no shadow. Since we know that the backboard casts an 11-foot shadow, the sun must be at an angle less than 45º (since the shadow is shorter than the height of the backboard).

We can use the inverse tangent function to find this angle:

angle = arctan(11/11)

angle = arctan(1)

angle ≈ 35.3º

Rounding to one decimal place, the answer is 35.0º, which corresponds to choice C.

The Height of an Outdoor Basketball Backboard Is Feet