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

Explanation:

Step1: Identify trigonometric relation

In right - triangle $RST$, $\cos T=\frac{ST}{RT}$.

Step2: Substitute known values

We know that $T = 46^{\circ}$ and $ST=\sqrt{10}$. So $\cos46^{\circ}=\frac{\sqrt{10}}{RT}$.

Step3: Solve for $RT$

$RT=\frac{\sqrt{10}}{\cos46^{\circ}}$. Since $\cos46^{\circ}\approx0.6947$ and $\sqrt{10}\approx3.1623$, then $RT=\frac{3.1623}{0.6947}\approx4.6$.

Answer:

$4.6$