Question

question
in $\triangle tuv$, the measure of $\angle v = 90^\circ$, $tv = 33$, $ut = 65$, and $vu = 56$. what ratio represents the cosine of $\angle u$?

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle U$

Adjacent to $\angle U$ is $VU = 56$, hypotenuse is $UT = 65$.

Step3: Write the cosine ratio

$\cos(\angle U) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{VU}{UT}$

Answer:

$\frac{56}{65}$