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To solve for \( x \) in this right triangle, where the angle is \( 37^\circ \) and the hypotenuse is 10 cm, we can use the cosine function. The cosine of an angle in a right triangle is defined as:

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

In this problem:
- \( \theta = 37^\circ \)
- Hypotenuse = 10 cm
- Adjacent side = \( x \)

Plugging in the values, we get:

\[
\cos(37^\circ) = \frac{x}{10}
\]

To solve for \( x \):

\[
x = 10 \cdot \cos(37^\circ)
\]

Using a calculator for \(\cos(37^\circ) \approx 0.7986\):

\[
x \approx 10 \cdot 0.7986 = 7.986 \, \text{cm}
\]

Rounding to the nearest hundredth:

\[
x \approx 7.99 \, \text{cm}
\]

### Final Answer:
\[
x = 7.99 \, \text{cm}
\]

Would you like a more detailed explanation or have any other questions?

### Related Questions:
1. How do you use the sine function to find a side in a right triangle?
2. What is the value of \(\sin(37^\circ)\) and how could it be used to find the other leg?
3. How can you find the hypotenuse if only the adjacent side and angle are known?
4. What is the difference between using sine, cosine, and tangent in trigonometry?
5. How can we verify the result using the Pythagorean theorem?

### Tip:
Always double-check if the calculator is in the correct mode (degrees vs. radians) when solving trigonometric problems.

Solve for x in the right triangle with a 10 cm hypotenuse and a 37-degree angle.

Learn how to solve for the adjacent side of a right triangle using the cosine of a 37° angle and a 10 cm hypotenuse. This solution covers key trigonometric concepts such as the cosine ratio and the Pythagorean theorem. Suitable for students in Grades 8-10.

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