Answer:
So, Carlos is approximately 1352 feet away from the base of the tree. Rounded to the nearest foot, Carlos is about 1352 feet away from the base of the tree.
Step-by-step explanation:
To find the distance from Carlos to the base of the tree, we can use trigonometry, specifically the tangent function.
The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side.
Let:
- \( h \) be the height of the tree (275 feet)
- \( d \) be the distance from Carlos to the base of the tree (what we want to find)
- \( \theta \) be the angle of elevation (11°)
- \( C \) be the height of Carlos (6 feet)
We can set up the following equation using tangent:
\[ \tan(\theta) = \frac{h - C}{d} \]
Substituting the given values:
\[ \tan(11^\circ) = \frac{275 - 6}{d} \]
We can now solve for \( d \):
\[ d = \frac{275 - 6}{\tan(11^\circ)} \]
Using a calculator:
\[ d ≈ \frac{269}{\tan(11^\circ)} ≈ \frac{269}{0.1989} ≈ 1352.1 \]
So, Carlos is approximately 1352 feet away from the base of the tree. Rounded to the nearest foot, Carlos is about 1352 feet away from the base of the tree.
