1. **State the problem:** We are given a right triangle TUV with a right angle at V. The side opposite angle V is 8 units, the hypotenuse is 15 units, and the side adjacent to angle T is 17 units. The problem states $\sin^{-1} \frac{8}{15} = m \angle T$ and asks us to analyze this. 2. **Recall the sine definition:** In a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$ for angle $\theta$. 3. **Identify the correct angle for $\sin^{-1} \frac{8}{15}$:** Since $\frac{8}{15}$ is opposite over hypotenuse, $\sin^{-1} \frac{8}{15}$ gives the measure of the angle whose opposite side is 8 and hypotenuse is 15. 4. **Check which angle this corresponds to:** The side opposite angle V is 8, so $\sin^{-1} \frac{8}{15}$ corresponds to $\angle V$, not $\angle T$. 5. **Conclusion:** The equation $\sin^{-1} \frac{8}{15} = m \angle T$ is incorrect because the opposite side to $\angle T$ is not 8, and the hypotenuse is 15. The correct statement is $m \angle V = \sin^{-1} \frac{8}{15}$. 6. **Additional note:** The side adjacent to $\angle T$ is given as 17, which is inconsistent with the triangle side lengths since the hypotenuse should be the longest side. This suggests a possible error in the triangle description. Final answer: $m \angle T \neq \sin^{-1} \frac{8}{15}$; instead, $m \angle V = \sin^{-1} \frac{8}{15}$.