In triangle PQR, we have \(\angle P = 90^\circ\), \(QR = 15\), and \(\tan R = 5\cos Q\). What is \(PQ\)?
Q
15
P R
tan R = 5 cos Q
QP / PR = 5 (QP / QR)
QP / PR = 5QP / 15
1/ PR = 5/ 15
1/ PR = 1/3
PR = 3
So
PQ = sqrt [ QR^2 - PR^2 ] = sqrt [ 15^2 - 3^2] = sqrt [ 225 - 9 ] = sqrt [216] = sqrt [36 * 6 ] = 6 sqrt (6)
