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The problem you provided describes a scenario where Teresa is standing 99 feet from the base of a leaning tree. The tree forms an angle of 87° with the ground, and the angle of elevation from where Teresa is standing to the top of the tree is 48°. We are tasked with finding the length of the tree \( x \).

This is a typical problem involving trigonometry, specifically the law of sines. Here's how to approach it:

### Step-by-step Solution:
1. **Sketch the situation**: You have a triangle formed by Teresa, the top of the tree, and the base of the tree. The known information includes:
   - The distance from Teresa to the base of the tree is 99 feet.
   - The angle between the ground and the leaning tree is \( 87^\circ \).
   - The angle of elevation from Teresa's position to the top of the tree is \( 48^\circ \).

2. **Using the Law of Sines**:
   To apply the Law of Sines, we first need the third angle of the triangle. The sum of angles in a triangle is always \( 180^\circ \), so:
   \[
   180^\circ - 87^\circ - 48^\circ = 45^\circ
   \]
   Now, we can use the Law of Sines:
   \[
   \frac{x}{\sin(48^\circ)} = \frac{99}{\sin(45^\circ)}
   \]
   Solving for \( x \), we get:
   \[
   x = \frac{99 \times \sin(48^\circ)}{\sin(45^\circ)}
   \]

3. **Calculate the values**:
   Using a calculator, we find:
   \[
   \sin(48^\circ) \approx 0.7431 \quad \text{and} \quad \sin(45^\circ) \approx 0.7071
   \]
   Substituting these values into the equation:
   \[
   x = \frac{99 \times 0.7431}{0.7071} \approx \frac{73.367}{0.7071} \approx 103.7 \, \text{feet}
   \]

### Final Answer:
The length of the tree is approximately **103.7 feet**.

Would you like a further breakdown of this solution? Here are five questions that expand on the topic:

1. How is the Law of Sines used in other types of real-world applications?
2. What other trigonometric laws are used in non-right triangles?
3. How would you solve this problem using the Law of Cosines?
4. Can you explain the importance of angle measurement in triangle problems?
5. How do you approximate values of sine for specific angles?

**Tip:** Always check the units of measurement before starting a trigonometry problem to avoid confusion.

Teresa is standing 99 feet from the base of a leaning tree. The tree forms an angle of 87° with the ground, and the angle of elevation from where Teresa is standing to the top of the tree is 48°. Find the length of the tree x.

Find the length of a leaning tree using trigonometric principles and the Law of Sines. Given a distance of 99 feet, an angle of elevation of 48°, and a 87° angle between the tree and the ground, calculate the tree's length with a step-by-step solution.

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