A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the base of the tree, what is the height of the tree?

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UpStudy AI · Accepted Answer

To determine the height of the tree, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the ratio of the opposite side (the height of the tree) to the adjacent side (the distance from the observer to the base of the tree).

Here's the step-by-step process:

1. **Define the Variables:**
   - Let $$ h $$ be the height of the tree.
   - The distance from the person to the base of the tree is $$ 10 $$ meters.
   - The angle of elevation is $$ 45^\circ $$.

2. **Use the Tangent Function:**
   $$
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
   $$
   Plugging in the known values:
   $$
   \tan(45^\circ) = \frac{h}{10}
   $$

3. **Solve for $$ h $$:**
   - We know that $$ \tan(45^\circ) = 1 $$.
   $$
   1 = \frac{h}{10}
   $$
   $$
   h = 10 \times 1 = 10 \text{ meters}
   $$

**Conclusion:**
The height of the tree is **10 meters**.
The tree is 10 meters tall.

A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the base of the tree, what is the height of the tree?

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