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

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for finding an angle in a triangle is $\cos T=\frac{s^{2}+u^{2}-t^{2}}{2su}$, where $s = 5$, $u=13$, and $t = 15$. So, $\cos T=\frac{5^{2}+13^{2}-15^{2}}{2\times5\times13}$.

Step2: Calculate the numerator and denominator

First, calculate the numerator: $5^{2}+13^{2}-15^{2}=25 + 169-225= - 31$. Then, calculate the denominator: $2\times5\times13 = 130$. So, $\cos T=\frac{-31}{130}\approx - 0.2385$.

Step3: Find the angle

$T=\cos^{-1}(-0.2385)$. Using a calculator, $T\approx103.8^{\circ}$.

Answer:

$103.8$