https://file.aiquickdraw.com/mathbot/file/1726456094843kcc1qkrp.jpg

The problem in the image asks to find the distance \( x \) using the **Law of Cosines**, where two sides of a triangle and the included angle are given.

Given:
- One side = 2.50 m
- Another side = 2.00 m
- The included angle = 100°.

The **Law of Cosines** formula is:

\[
x^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]

Where:
- \( a = 2.50 \, \text{m} \)
- \( b = 2.00 \, \text{m} \)
- \( C = 100^\circ \)

Plugging in the values, we can form the equation to solve for \( x \):

\[
x^2 = (2.50)^2 + (2.00)^2 - 2(2.50)(2.00) \cdot \cos(100^\circ)
\]

Now let's check the answer options:

- **A:** This option correctly follows the Law of Cosines structure, but the angle should be subtracted, not added.
- **B:** This is the correct form of the equation based on the Law of Cosines.
- **C:** The subtraction is misplaced; it doesn't follow the structure properly.
- **D:** The square root is applied too early; the Law of Cosines formula gives \( x^2 \), so we square both sides later.

Hence, **B** is the correct choice.

Would you like a detailed breakdown of solving this equation or have any questions?

### Related questions:
1. What is the cosine of 100°?
2. How does the Law of Cosines differ from the Pythagorean theorem?
3. Why is the angle of 100° important in this problem?
4. How would this problem change if the angle were 90°?
5. What other real-world applications involve the Law of Cosines?

### Tip:
The Law of Cosines is useful for solving triangles when two sides and an included angle are known, or when all three sides are known.

Use the law of cosines to solve the following problem. The robot arm shown in the figure places packages on a conveyor belt. What is the distance x?

Learn how to solve a geometry problem involving the Law of Cosines. The robot arm places packages on a conveyor belt. Given two sides of a triangle and an included angle, find the distance x using the Law of Cosines.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation