https://file.aiquickdraw.com/mathbot/file/1736749502117lzkmw0y6.jpg

The problem in the image asks to solve for \( x \), given a right triangle where:

- \( \angle E \) is \( 62^\circ \),
- the side adjacent to \( 62^\circ \) is \( 15 \),
- \( x \) is the hypotenuse.

We can solve this using the cosine function, since cosine relates the adjacent side and the hypotenuse in a right triangle:

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

### Step 1: Write the equation
\[
\cos(62^\circ) = \frac{15}{x}
\]

### Step 2: Solve for \( x \)
Rearrange the equation:
\[
x = \frac{15}{\cos(62^\circ)}
\]

### Step 3: Calculate \( \cos(62^\circ) \)
Using a calculator:
\[
\cos(62^\circ) \approx 0.4695
\]

### Step 4: Substitute and solve
\[
x = \frac{15}{0.4695} \approx 31.9
\]

### Final Answer:
\[
x \approx 31.9 \text{ (rounded to the nearest tenth)}
\]

Would you like a more detailed explanation or assistance with related concepts? 

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Here are 5 related questions to explore:
1. How can you determine which trigonometric ratio to use for a given problem?
2. What is the relationship between sine, cosine, and tangent in right triangles?
3. How would you solve for the opposite side in a similar triangle problem?
4. How does the angle size affect the cosine value?
5. What are other methods to verify the solution in trigonometry?

**Tip**: Always double-check the units (degrees vs radians) when using trigonometric functions in a calculator!

Solve for x. Round to the nearest tenth, if necessary. A right triangle is shown where angle E is 62°, the adjacent side is 15, and the hypotenuse is x.

Learn how to solve for the hypotenuse in a right triangle using the cosine function. Given a 62° angle and an adjacent side of 15, calculate the hypotenuse and round to the nearest tenth. This trigonometry problem is suitable for Grades 9-10.

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