Final answer:
Using trigonometry with the tangent function and the given angle of elevation, the height of the pine tree is approximately calculated to be 38.9 feet, which suggests the closest answer to be option (b) 43.2 ft.
Step-by-step explanation:
To find the height of the pine tree, we can use trigonometry, specifically the tangent function, since the tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tree) to the adjacent side (the length of the shadow on the ground).
The angle of elevation of the sun is given as 24°25'. First, we need to convert this to a decimal degree. There are 60 minutes in a degree, so 25 minutes is 25/60 degrees, which is approximately 0.4167 degrees. Therefore, the angle in decimal degrees is 24 + 0.4167 = 24.4167 degrees.
Quick review: The tangent of an angle θ is defined as tan(θ) = opposite/adjacent. In this case, the opposite side is the height of the tree (H), and the adjacent side is the length of the shadow (86 feet).
Applying trigonometry, we have:
tan(24.4167°) = H / 86 feet
H = 86 feet × tan(24.4167°)
Calculating this gives us:
H ≈ 86 feet × 0.4524 (Value of tan(24.4167°) approximately)
H ≈ 38.9 feet
The closest answer to 38.9 feet from the given options is 43.2 ft, making option (b) the most likely correct choice. However, note that none of the options provided exactly match the calculated value, so you should double-check your calculations or consult your teacher for clarification if this question is from a test.