https://r2.erweima.ai/mathbot/image/1720058231206g3b2xnzq.png

To find the length of side \( x \) in the given right triangle where one angle is \( 42^\circ \) and the hypotenuse is 12, we can use trigonometric functions.

Given:
- Hypotenuse = 12
- Angle = \( 42^\circ \)

We use the cosine function, defined as:
\[ \cos(42^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Thus,
\[ \cos(42^\circ) = \frac{x}{12} \]

Rearranging to solve for \( x \):
\[ x = 12 \cos(42^\circ) \]

Using a calculator to find \( \cos(42^\circ) \):
\[ \cos(42^\circ) \approx 0.7431 \]

Now, multiply by 12:
\[ x \approx 12 \times 0.7431 \approx 8.9172 \]

Therefore, the length of side \( x \) is approximately \( 8.92 \) units.

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:

1. How can we find the length of the other side of the triangle?
2. What is the sine of the \( 42^\circ \) angle?
3. How do we verify the side lengths using the Pythagorean theorem?
4. What is the tangent of the \( 42^\circ \) angle?
5. How do we calculate the area of this right triangle?

**Tip:** Remember that for right triangles, the cosine of an angle gives the ratio of the adjacent side to the hypotenuse.

Learn how to find the length of side x in a right triangle where one angle is 42 degrees and the hypotenuse is 12 units. Step-by-step solution using trigonometric functions and cosine. Suitable for high school students studying trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation