Question

find the cosine of ∠u. simplify your answer and write it as a proper fraction, improper fraction, or whole number. cos(u) =

Explanation:

Step1: Recall cosine ratio in right - triangle

In right - triangle $\triangle TUV$ with right - angle at $T$, $\cos(U)=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify adjacent and hypotenuse

The side adjacent to $\angle U$ is $TU$, and the hypotenuse is $UV$. First, find $TU$ using the Pythagorean theorem. Let $TU = x$, then $x=\sqrt{UV^{2}-TV^{2}}=\sqrt{74^{2}-70^{2}}=\sqrt{(74 + 70)(74 - 70)}=\sqrt{144\times4}=\sqrt{576}=24$.

Step3: Calculate $\cos(U)$

The side adjacent to $\angle U$ is $24$ and the hypotenuse is $74$. So, $\cos(U)=\frac{24}{74}=\frac{12}{37}$.

Answer:

$\frac{12}{37}$