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

Answer:

$3.3$

Explanation:

Step1: Identify trig - ratio

In right - triangle $TUV$ with right - angle at $T$, we know $\sin V=\frac{opposite}{hypotenuse}$. Here, $\angle V = 36^{\circ}$, the side opposite to $\angle V$ is $TU$ and the hypotenuse $UV = 5.6$.

Step2: Apply sine formula

We have $\sin V=\sin36^{\circ}=\frac{TU}{UV}$. Since $UV = 5.6$, then $TU=UV\times\sin36^{\circ}$.

Step3: Calculate value

We know that $\sin36^{\circ}\approx0.5878$. So, $TU = 5.6\times0.5878=3.29168\approx3.3$.