In triangle XYZ, we have angle X = 90 and tan Y = 3/2. If YZ = 80, then what is XY?
Y
80
X Z
tan Y = 3/2 = XZ / XY then XZ = (3/2)XY
So
(XY)^2 + [(3/2) XY]^2 = 80^2
XY^2 + (9/4)XY^2 = 6400
(13/4)XY^2 = 6400
XY^2 = 6400 ( 4 /13)
XY^2 = (6400 * 4) / 13
XY = 80 * 2 / sqrt (13)
XY = 160/ sqrt (13)
