In triangle XYZ, we have ngle X = 90 degrees and tan Z = 7. If YZ = 100, then what is XY?
Y
X Z
Mmmm.....let's see
YZ = 100
If the tan Z = 7
This indicates that XY / XZ = 7
So this implies that XY = 7XZ ⇒ XY/7 = XZ
So....using the Pythagorean Theorem we know that
YZ = √ [ XY^2 + XZ^2] subbing, we have that
100 = √ [ XY^2 + (XY/7)^2 ] simplify
100 = √ [XY^2 + XY^2 / 49 ]
100 = √ [ 49XY^2 + XY^2 ] / 7 multiply both sides by 7
700 = √]50 XY^2] square both sides
490000 = 50 XY^2 divide both sides by 50
9800 = XY^2 take the positive root
XY = √9800 = √[4900 * 2 ] = 70√2