https://file.aiquickdraw.com/mathbot/file/17292076798818amo464j.jpg

The image shows a right-angled triangle where:

- \( B = 29^\circ \) (angle \( B \)),
- \( a = 9 \) (the length of the opposite side to angle \( B \)),
- \( c \) (the hypotenuse) is the value to determine.

To find the length of the hypotenuse \( c \), we can use the sine function, which relates the opposite side and the hypotenuse:

\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}
\]

Substitute the known values:

\[
\sin(29^\circ) = \frac{9}{c}
\]

Solving for \( c \):

\[
c = \frac{9}{\sin(29^\circ)}
\]

Now, calculate \( \sin(29^\circ) \) using a calculator:

\[
\sin(29^\circ) \approx 0.4848
\]

So,

\[
c = \frac{9}{0.4848} \approx 18.56
\]

Thus, the value of \( c \), rounded to two decimal places, is **18.56**.

Would you like more details or have any questions about this solution?

Here are some related questions you might find useful:
1. How would you solve for side \( b \) using trigonometric functions?
2. What is the value of \( \cos(B) \) for this triangle?
3. How does the sine function change as the angle increases?
4. What is the relationship between the angles in a right triangle?
5. Can you use the Pythagorean theorem to verify the solution?

**Tip:** In right-angled triangles, sine, cosine, and tangent functions are very helpful in finding missing sides or angles when given partial information.

If B = 29° and a = 9, determine the value of c. Round to two decimal places.

Learn how to determine the value of the hypotenuse in a right-angled triangle with angle B = 29° and side a = 9. This problem involves using the sine function and trigonometric ratios. Suitable for students in Grades 9-11.

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