Let's determine the angle of elevation from your position to the top of the 48-foot tall palm tree.
First, let's define the problem parameters:
- Distance from the tree (adjacent side of the right triangle): 60 feet
- Height of the tree (opposite side of the right triangle): 48 feet
We can use trigonometry to find the angle of elevation. Specifically, the tangent function, which relates the opposite side to the adjacent side in a right triangle, is useful here:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Substitute the known values into the equation:
[tex]\[ \tan(\theta) = \frac{48}{60} \][/tex]
Now calculate the ratio:
[tex]\[ \tan(\theta) = 0.8 \][/tex]
To find the angle [tex]\(\theta\)[/tex], we take the inverse tangent (arctan) of 0.8:
[tex]\[ \theta = \arctan(0.8) \][/tex]
Using a calculator or trigonometric table to find the inverse tangent, we get:
[tex]\[ \theta \approx 38.7^\circ \][/tex]
So, the angle of elevation from your position to the top of the tree, rounded to the nearest tenth, is [tex]\(38.7^\circ\)[/tex].
Therefore, the correct answer is:
d. [tex]\( 38.7^\circ \)[/tex]
