Determine the ratio equivalent to cos Q.

Work Shown:

The triangles are similar, which means the corresponding angles are congruent. In this case, we can say angle K = angle Q. Note how K and Q are the second letters of JKL and PQR respectively. The order matters.

Because angle K = angle Q, we can use information from triangle JKL to get information about triangle PQR.

We can say the following:

cos(angle) = adjacent/hypotenuse

cos(K) = LK/JK

cos(K) = 5/13

cos(Q) = 5/13 ... plug in K = Q