To solve this problem, we will use trigonometry, specifically the tangent function. But first, let's imagine the scenario and draw a diagram.
Since we can't draw an actual diagram in this format, I'll describe it instead:
1. Visualize the scenario as a right triangle, where:
- The tree forms the opposite side (the side opposite to the angle of elevation).
- The ground forms the adjacent side (the side adjacent to the angle of elevation, on the ground).
- The line of sight from the point on the ground to the top of the tree forms the hypotenuse.
2. The angle of elevation from the ground to the top of the tree is given as 35°. This angle is at the point on the ground where an observer is looking up to the top of the tree.
3. The distance from the observer to the foot of the tree along the ground is 47 feet.
Now, we'll label the triangle with the given information:
- Let \( h \) be the height of the tree.
- The ground distance from the observer to the tree is \( 47 \) feet.
- The angle of elevation is \( 35° \).
Next, we will write down the trigonometric ratio that involves the opposite side and the adjacent side, which is the tangent (tan) function:
\[ \tan(\theta) = \frac{\text{opposite side (height of the tree, } h)}{\text{adjacent side (ground distance, } 47 \text{ feet)}} \]
We have:
\[ \tan(35°) = \frac{h}{47} \]
Now, we want to solve for \( h \):
\[ h = 47 \cdot \tan(35°) \]
We need to use a calculator to find the tangent of 35°. Typically, calculators require angles to be in radians, but since we're using degrees, most scientific calculators will have a degree mode that we can use.
Once we calculate \( \tan(35°) \), we multiply that by \( 47 \):
\[ h = 47 \cdot \tan(35°) \approx 47 \cdot 0.7002 \approx 32.9094 \]
Finally, we round the result to the nearest tenth:
\[ h \approx 32.9 \text{ feet} \]
Thus, the height of the tree is approximately 32.9 feet.
