https://file.aiquickdraw.com/mathbot/file/1727087608812m4m89pol.jpg

The given image shows a right triangle \( \triangle ABC \), where:

- \( \angle A = 24^\circ \)
- \( \overline{AB} = 116 \) inches (the hypotenuse)
- \( \overline{b} \) represents the unknown side adjacent to \( \angle A \)

We need to find the value of \( b \), which is the side adjacent to \( \angle A \).

To solve for \( b \), we can use the **cosine** function, since:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Here, \( \theta = 24^\circ \), the adjacent side is \( b \), and the hypotenuse is 116 inches. Thus, the equation becomes:

\[
\cos(24^\circ) = \frac{b}{116}
\]

Solving for \( b \):

\[
b = 116 \times \cos(24^\circ)
\]

Let me calculate that for you.The length of side \( b \) (the side adjacent to the 24° angle) is approximately **106 inches**.

Would you like any further details or explanations? Here are some related questions:

1. How do you use the sine function in similar problems?
2. What if you needed to solve for the opposite side of the triangle?
3. How can the Pythagorean Theorem verify your result?
4. What are some practical uses of trigonometry in real-life scenarios?
5. How does angle size affect the length of triangle sides?

**Tip:** Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems.

Find the measure of the side of the right triangle whose length is designated by a lowercase letter b. The hypotenuse is 116 inches, and the angle adjacent to side b is 24°. Round the answer to the nearest whole number.

Learn how to find the adjacent side of a right triangle when given the hypotenuse and an angle. This problem uses the cosine function and involves solving b = 116 × cos(24°). Suitable for students in Grades 9-11.

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