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The given problem shows a right triangle where one angle is \( 62^\circ \), the adjacent side to this angle is \( 5.3 \, \text{cm} \), and we need to find the hypotenuse labeled as \( x \).

We can use trigonometry to solve this. Specifically, we use the cosine function, since:

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

Given:
\[
\theta = 62^\circ, \quad \text{adjacent} = 5.3 \, \text{cm}, \quad \text{hypotenuse} = x
\]

Using the formula:
\[
\cos(62^\circ) = \frac{5.3}{x}
\]

Now solve for \( x \):
\[
x = \frac{5.3}{\cos(62^\circ)}
\]

Calculating \( \cos(62^\circ) \) (using a calculator):
\[
\cos(62^\circ) \approx 0.4695
\]

Substitute this value into the equation:
\[
x = \frac{5.3}{0.4695} \approx 11.29 \, \text{cm}
\]

Thus, the length of the side labeled \( x \) is approximately \( 11.29 \, \text{cm} \).

Would you like further details or have any questions?

Here are some related questions:
1. How would you solve for \( x \) if you were given a different angle?
2. Can you use the sine function instead? If so, how?
3. What is the sine of \( 62^\circ \), and how would it relate to this problem?
4. How would you solve for the opposite side if that was missing?
5. What does the tangent function represent in a right triangle?

**Tip:** Always double-check if you're using the correct trigonometric function by identifying the opposite, adjacent, and hypotenuse sides relative to the given angle.

Calculate the length of the side labeled x in a right triangle where one angle is 62° and the adjacent side to this angle is 5.3 cm.

Solve a trigonometry problem involving a right triangle with a 62° angle and an adjacent side of 5.3 cm. Learn how to apply the cosine function to calculate the hypotenuse. Suitable for students in Grades 9-10.

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