Question

5.2 part 2
score: 2/10 answered: 2/10
question 3
find the height of a pine tree that casts a 77 - foot shadow on the ground if the angle of elevation of the sun is 23°9. round to the nearest tenth.
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Explanation:

Step1: Convert the angle from degrees and minutes to decimal degrees

Since \(1^{\circ}=60'\), then \(9'=\frac{9}{60}=0.15^{\circ}\). So \(23^{\circ}9' = 23.15^{\circ}\).

Step2: Use the tangent function

Let \(h\) be the height of the tree. We know that \(\tan\theta=\frac{opposite}{adjacent}\). Here, \(\theta = 23.15^{\circ}\), the adjacent side (shadow length) \(x = 77\) feet, and the opposite side is the height \(h\) of the tree. So \(\tan(23.15^{\circ})=\frac{h}{77}\).
Then \(h = 77\times\tan(23.15^{\circ})\).
Using a calculator, \(\tan(23.15^{\circ})\approx0.427\).
So \(h=77\times0.427 = 32.879\approx32.9\)

Answer:

\(32.9\)