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We can solve this problem using trigonometric functions since the given triangle is a right triangle. We are provided with:

- One angle: \( 59^\circ \)
- The adjacent side to the angle (15 inches)
- We need to find the hypotenuse, labeled \( a \).

To find \( a \), we can use the **cosine** function, which relates the adjacent side to the hypotenuse in a right triangle:

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

For this triangle:

\[
\cos(59^\circ) = \frac{15}{a}
\]

Now, solving for \( a \):

\[
a = \frac{15}{\cos(59^\circ)}
\]

Let me calculate the value of \( a \).The length of the hypotenuse \( a \) is approximately \( 29.12 \) inches (rounded to two decimal places).

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would you solve for the opposite side of the triangle using trigonometry?
2. What happens if you are given the opposite side instead of the adjacent side?
3. How can you verify the solution using the Pythagorean theorem?
4. How would the solution change if the given angle were larger or smaller?
5. What other trigonometric functions could be used for similar problems?

**Tip:** When solving right triangle problems, always double-check if you're using the correct trigonometric ratio (sine, cosine, or tangent) based on the given sides and angle.

For the right triangle below, find the length of a.

Learn how to find the length of the hypotenuse of a right triangle with a 59° angle and an adjacent side of 15 inches. This problem uses the cosine function to solve for the missing side. Suitable for students in Grades 9-11.

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