To find the measure of angle $x$, we use trigonometry. The given right triangle has:

• Hypotenuse = 31
• Adjacent side (to angle $x$) = 24

We use the cosine function:

$\cos x = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{24}{31}$

Now, solving for $x$:

$x = \cos^{-1} \left(\frac{24}{31}\right)$

Using a calculator:

$x = \cos^{-1} (0.7742)$

$x \approx 39.57^\circ$

Final Answer:

$x \approx 39.57^\circ$

Would you like further details or explanations?

Related Questions:

1. How do you find an angle using the sine function?
2. How do you find the third side of a right triangle using the Pythagorean theorem?
3. How would you find the other non-right angle in the triangle?
4. What are the basic trigonometric ratios and when should each be used?
5. How can trigonometry be applied in real-world problems?

Tip:

Always check if your calculator is in degree mode when solving for angles in degrees!