Question

find the cosine of $\angle h$.
write your answer in simplified, rationalized form. do not round.
$\cos(h) = $

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 $\angle H$

Adjacent side to $\angle H$: $HG = 8$; Hypotenuse: $HF = \sqrt{87}$

Step3: Substitute values into formula

$\cos(H) = \frac{8}{\sqrt{87}}$

Step4: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{87}$:
$\cos(H) = \frac{8 \times \sqrt{87}}{\sqrt{87} \times \sqrt{87}} = \frac{8\sqrt{87}}{87}$

Answer:

$\frac{8\sqrt{87}}{87}$