find the cosine of $angle h$.\nsimplify your answer and write it as a proper fraction, improper fraction, or…

find the cosine of $angle h$.\nsimplify your answer and write it as a proper fraction, improper fraction, or whole number.\n$cos(h) = square$

find the cosine of $angle h$.\nsimplify your answer and write it as a proper fraction, improper fraction, or whole number.\n$cos(h) = square$

Answer

Explanation:

Step1: Find side $HG$ via Pythagoras

$$HG = \sqrt{FH^2 - FG^2} = \sqrt{13^2 - 12^2} = \sqrt{169-144} = \sqrt{25} = 5$$

Step2: Identify cosine components for $\angle H$

For $\angle H$, adjacent side = $HG=5$, hypotenuse = $FH=13$. Cosine is $\frac{\text{adjacent}}{\text{hypotenuse}}$. $$\cos(H) = \frac{HG}{FH} = \frac{5}{13}$$

Answer:

$\frac{5}{13}$