find m∠t. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠t = °

Explanation:

Step1: Recall trigonometric ratio

In right - triangle $UST$, $\sin T=\frac{US}{UT}$. Here, $US = 6$ and $UT=9$.

Step2: Calculate sine of angle T

$\sin T=\frac{6}{9}=\frac{2}{3}$.

Step3: Find the measure of angle T

$T=\sin^{- 1}(\frac{2}{3})$. Using a calculator, $T=\sin^{-1}(\frac{2}{3})\approx41.8^{\circ}$.

Answer:

$41.8$