Question

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

Explanation:

Step1: Identify congruent triangles

Triangles $\triangle IJK$ and $\triangle HGF$ are right triangles with corresponding sides equal, so $\angle F \cong \angle K$. We can find $\cos(K)$ first.

Step2: Recall cosine definition for right triangles

For a right angle, $\cos(\theta)=\frac{\text{adjacent side}}{\text{hypotenuse}}$. For $\angle K$, adjacent side is $JK=8$, hypotenuse is $IK=17$.

Step3: Calculate $\cos(K)$ (equal to $\cos(F)$)

$\cos(F)=\cos(K)=\frac{8}{17}$

Answer:

$\frac{8}{17}$