Question

find the cosine of ∠u.

write your answer in simplified, rationalized form. do not round.
cos (u) =

Explanation:

Step1: Recall cosine definition for right triangles

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

Step2: Identify sides for $\angle U$

Adjacent side to $\angle U$: $SU = 4$; Hypotenuse: $TU = \sqrt{89}$.

Step3: Substitute values into formula

$\cos(U)=\frac{4}{\sqrt{89}}$

Step4: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{89}$:
$\cos(U)=\frac{4\times\sqrt{89}}{\sqrt{89}\times\sqrt{89}}=\frac{4\sqrt{89}}{89}$

Answer:

$\frac{4\sqrt{89}}{89}$