express cos t as a fraction in simplest terms.

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle T$, the adjacent side to $\angle T$ is $UT$ and the hypotenuse is $VT$.

Step2: Identify the sides

We are given $UT = \sqrt{78}$ and $VT=28$.

Step3: Calculate $\cos T$

$\cos T=\frac{UT}{VT}=\frac{\sqrt{78}}{28}$. Since $\sqrt{78}$ and $28$ have no common factors other than 1, the fraction is already in simplest terms.

Answer:

$\frac{\sqrt{78}}{28}$