The images you've uploaded show two different trigonometry problems.

1. The first image involves solving for the sine of an angle $X$ in a right triangle. Using the given sides, the opposite side and hypotenuse, the process involves:

   • Using the Pythagorean Theorem to find the missing leg.
   • Applying the sine function formula $\sin(X) = \frac{\text{opposite}}{\text{hypotenuse}}$.
   • The opposite side $\sqrt{23}$ and the hypotenuse is 6, resulting in the approximate value of $0.8$.

2. The second image presents a similar problem where you are asked to find $\cos(S)$ for another triangle with one side of length $\sqrt{7}$ and the hypotenuse of length 22. The steps to solve this would be:

   • First, use the Pythagorean Theorem to find the missing leg.
   • Then apply the cosine function formula $\cos(S) = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Would you like me to walk you through the solution to the second problem, or would you like help with a specific part? Let me know if you have any questions about either problem.

Related Questions:

1. How do you apply the Pythagorean Theorem in other types of problems?
2. Can you explain how to find the other trigonometric ratios like tangent, secant, etc.?
3. How do you use trigonometric functions in non-right triangles?
4. What are the differences between the sine, cosine, and tangent functions?
5. What are some real-life applications of trigonometry?

Tip:

Remember, for any right triangle, you can use SOH-CAH-TOA to recall the trigonometric identities:

• Sine (SOH): Opposite / Hypotenuse
• Cosine (CAH): Adjacent / Hypotenuse
• Tangent (TOA): Opposite / Adjacent