https://file.aiquickdraw.com/mathbot/file/1726072048445bpx5zhpi.jpg

To solve for \( x \) in the given right triangle, we can use trigonometric ratios. Here’s how to proceed:

- The given triangle has:
  - Angle: \( 32^\circ \)
  - Hypotenuse: \( 15 \)
  - We are tasked with finding the length of the side adjacent to the \( 32^\circ \) angle, labeled \( x \).

We can use the cosine function, which is defined as:

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

Substitute the known values:

\[
\cos(32^\circ) = \frac{x}{15}
\]

Now, solve for \( x \):

\[
x = 15 \cdot \cos(32^\circ)
\]

Let me calculate that for you.The length of \( x \) is approximately \( 12.72 \) units.

Would you like further clarification on any part of this solution?

Here are some related questions to deepen your understanding:
1. How would you find the length of the opposite side of the triangle?
2. What trigonometric ratio could be used if you knew the opposite side instead of the hypotenuse?
3. How does the angle size affect the adjacent side's length?
4. What is the relationship between sine, cosine, and tangent in right triangles?
5. How would the formula change if the triangle was not a right triangle?

**Tip:** When solving right triangles, always double-check which trigonometric function relates the sides you are given to the angle.

For the right triangle below, find the length of x.

Learn how to find the length of x in a right triangle with a given angle of 32° and hypotenuse of 15 units. This problem uses the cosine function, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation