A certain flagpole that is 298 feet tall casts a shadow 138 feet long. Find the angle of elevation of the sun.

Answer 1

The answer is tan^-1(298/138)=65.15 degrees.

The tricky part of this problem is recognizing that we need to form a triangle and pick the correct angle to measure. The first step is to draw a shape with the information that is given in the problem.

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| 298ft

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138ft

What we have drawn is the height and width of a right triangle.

Now since we are measuring the angle of the sun, it may be helpful to draw the sun here.

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\ ___ /

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/ |>

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/ | 298ft

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138ft

As you can see here, if we trace the sun's ray from the tip of the flag to the farthest point of the shadow we form the hypotenuse of our right triangle

Also notice how if we measure the angle from the tip of the flag's shadow to the tip of the flag we will also get the angle to the elevation of the sun.

I will make that angle with an "x"

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/ |

/ | 298ft

/x__|

138ft

Since we have two known sides and an unknown angle, we can use the "Soh Cah Toa" Technique

Sin(x)= Opposite/ Hypotenuse

Cos(x)= Adjacent/Hypotenuse

Tan(x)= Opposite/Adjacent

We have an opposite side from x (298ft)

and we have an adjacent side to x (138ft)

So should use Tan here.

This gives us Tan(x)= (298ft/138ft)

To solve for x we simply need to use Tan^-1 to solve for x

Tan^-1(298ft/138ft) = x

x = 65.15 Degrees