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We are given a right triangle with a hypotenuse of 16 units, an opposite side of 10 units, and we are tasked with finding the angle \( x^\circ \) using SOHCAHTOA.

SOHCAHTOA represents the trigonometric ratios:
- **S**ine: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)
- **C**osine: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
- **T**angent: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

Since we know the opposite (10) and the hypotenuse (16), we use the sine function:

\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{16} = 0.625
\]

Now, find the angle \( x \) by taking the inverse sine (\( \sin^{-1} \)) of 0.625:

\[
x = \sin^{-1}(0.625)
\]

Let me calculate that.The angle \( x \) is approximately \( 38.7^\circ \) when rounded to the nearest tenth.

Do you need further details or have any questions? Here are some related questions for deeper understanding:

1. What is the significance of SOHCAHTOA in solving right triangles?
2. How can you use the cosine or tangent functions to verify the answer?
3. Can you calculate the remaining angle of the triangle?
4. How does the Pythagorean theorem confirm the side lengths of the triangle?
5. What is the inverse sine function, and why is it used here?

**Tip:** Always remember that SOHCAHTOA applies only to right-angled triangles.

Use SOHCAHTOA to solve for the missing angle in a right triangle with a hypotenuse of 16 units and an opposite side of 10 units. Round your answer to the nearest tenth.

Use SOHCAHTOA to find the missing angle in a right triangle with a hypotenuse of 16 units and an opposite side of 10 units. Learn how to apply the sine function and inverse trigonometric functions to solve for the angle, and round your answer to the nearest tenth. Suitable for students in Grades 8-10.

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