Final answer:
The length of the shadow cast by Paul, when the angle of elevation of the sun is 36° and Paul is 5.8 ft. tall, is approximately 7.98 ft. (Option D is the closest: 7.4 ft).
The correct option is D.
Step-by-step explanation:
To find the length of the shadow (s), we can use trigonometry. The tangent of the angle of elevation (theta) is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. In this case:
tan(theta) = height / length of shadow
Given that the angle of elevation (\(\theta\)) is 36° and the height of Paul (height}) is 5.8 ft, we can rearrange the equation to solve for the length of the shadow (s):
s =height / {tan(theta)}
s = {5.8 ft / {tan(36^\circ)}
Now, calculate s:
s ≈ {5. ft} / {0.7265}
s ≈ 7.98ft
So, the length of the shadow is approximately 7.98 feet.
None of the provided options (A, B, C, D) exactly match the calculated value, but the closest option is D) 7.4 ft. Keep in mind that the discrepancy may be due to rounding or the options provided.
The correct option is D.