https://file.aiquickdraw.com/mathbot/file/1726203791544xue5b44d.jpg

The image shows a right triangle with an angle of \(49^\circ\), a side labeled as 20, and an unknown side labeled as \(x\). We can use trigonometric functions to solve for \(x\).

### Step-by-Step Solution:

Given:
- \(\angle H = 49^\circ\)
- Adjacent side = 20 (since it's adjacent to \(\angle H\))
- Hypotenuse = \(x\) (since it's opposite the right angle)

Using the cosine function, which relates the adjacent side and the hypotenuse:
\[
\cos(49^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{20}{x}
\]

Now, solve for \(x\):
\[
x = \frac{20}{\cos(49^\circ)}
\]

Let me calculate this for you.The value of \(x\), the hypotenuse of the triangle, is approximately 30.5 when rounded to the nearest tenth.

Do you have any questions or would you like further details?

Here are 5 related questions to explore:
1. How can you use the sine function to solve for the opposite side of the triangle?
2. What would change if the given angle was larger or smaller?
3. How do you determine when to use sine, cosine, or tangent in solving triangles?
4. Can you calculate the length of the other side using the Pythagorean theorem?
5. What are some real-life applications of trigonometry in right triangles?

**Tip:** When solving right triangles, always start by identifying which sides correspond to the opposite, adjacent, or hypotenuse relative to the given angle.

Solve for x in the right triangle with an angle of 49° and an adjacent side of 20.

Learn how to solve for the hypotenuse of a right triangle given an angle of 49° and an adjacent side length of 20 using the cosine function. This problem covers key trigonometric concepts, including trigonometric ratios and their application in right triangles. Suitable for students in Grades 9-12.

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