Question

What is the angle of elevation of the sun if a 45 foot tall flag pole casts a 22 foot long shadow?A. 63.9B. 60.7C. 26.1D. 29.3

Answer 1

From the shadow of the flagpole, we can build a right triangle that will allow us to estimate the angle of elevation of the sun.

The shadow on the ground will be one hick of the triangle, and the flagpole will be the other hick. The hypotenuse will be the line connecting the tip of the flagpole and the tip of the shadow. The angle of elevation is the one formed between the ground and the hypotenuse.

With that, the adjacent hick will be the shadow in the ground (22 ft long), and the opposite hick is the flagpole itself (45 ft tall). The tangent of an angle is the ratio of the opposite hick to the adjacent hick. Let's call the angle of elevation α. Then:

`\tan \alpha=(45ft)/(22ft)`

To find the value of α we use the function inverse tangent:

`\begin{gathered} \alpha=\tan ^(-1)(45)/(22) \\ \\ \alpha\approx63.9 \end{gathered}`

Then, the angle of elevation is approximately 63.9°. The correct answer is option A.