Question

question 4
1 pts
solve. round answers to the nearest tenth when necessary (one decimal place).
a 50-foot tree is cut 10 feet above the ground. the top of the tree stays attached but crashes to the ground to form a triangle. what is the measure of the angle formed where the tree was cut?
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Explanation:

Step1: Identify triangle sides

The standing part of the tree is $10$ ft, the fallen top is $50 - 10 = 40$ ft (hypotenuse), and the ground distance is the other leg. We use the cosine function for the angle at the cut: adjacent side = 10 ft, hypotenuse = 40 ft.

Step2: Apply cosine formula

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{10}{40} = 0.25$

Step3: Calculate inverse cosine

$\theta = \cos^{-1}(0.25)$
Using a calculator, $\theta \approx 75.5^\circ$

Answer:

$75.5$