IDNLearn.com is your go-to platform for finding accurate and reliable answers. Get prompt and accurate answers to your questions from our experts who are always ready to help.
Sagot :
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]
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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.