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We are given that:

\[
\sin(X) = \frac{8}{15}
\]

To find the measure of angle \( X \), we use the inverse sine function (also known as arcsin):

\[
X = \sin^{-1} \left( \frac{8}{15} \right)
\]

Now, let's calculate the value of \( X \) in degrees, rounding to the nearest tenth.

I'll compute that for you.The measure of angle \( X \) is approximately \( 32.2^\circ \), rounded to the nearest tenth of a degree.

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How can we calculate the cosine of angle \( X \) based on the given sine value?
2. How would you find \( X \) if given \( \cos(X) \) instead?
3. What is the value of \( \tan(X) \) based on the given sine value?
4. Can this value of \( \sin(X) \) be used to determine side lengths in a right triangle?
5. How can inverse trigonometric functions help in solving real-world problems?

**Tip:** Always ensure your calculator is in the correct mode (degrees or radians) depending on the context of the problem.

Find the measure of the angle given Sin(X) = 8/15. Round to the nearest tenth of a degree.

Learn how to find the angle measure when Sin(X) = 8/15 using the inverse sine function. This trigonometry problem is suitable for high school students (Grades 10-12) and includes a step-by-step solution with an answer rounded to the nearest tenth of a degree.

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