To find the angle formed from the top of the tree, we can use trigonometry. Specifically, we can use the sine function, which relates the opposite side and hypotenuse of a right triangle.
Let:
- \( h = 34 \) feet (the height of the tree),
- \( d = 47 \) feet (the length of the line from the top of the tree to the top of the shadow).
We can find the angle \( \theta \) at the top of the tree using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{d} = \frac{34}{47} \]
Now, we calculate \( \frac{34}{47} \):
\[ \frac{34}{47} \approx 0.7234 \]
To find the angle \( \theta \), we take the inverse sine (also known as arcsine) of the value:
\[ \theta = \arcsin(0.7234) \]
Using a calculator,
\[ \theta \approx 46.65^\circ \]
Rounding to the nearest whole degree, we find:
\[ \theta \approx 47^\circ \]
Thus, the angle formed from the top of the tree is approximately 47 degrees.
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