The computations to find the other two side lengths are summarized in the following table.
Points
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Length
X( 2, 2) and Y( 2, -2)
XY = sqrt(( 2- 2)^2 + ( -2- 2)^2)
XY = 4
Y( 2, -2) and Z( 7, -2)
YZ = sqrt(( 7- 2)^2 + ( -2-( -2))^2)
YZ = 5
Since XY^2+YZ^2 = XZ^2, we conclude that △ XYZ is a right triangle with ∠Y being the right angle.
Next, applying the tangent ratio, we can write the following equation involving the measure of ∠X.
tan X = YZ/XY
⇒
tan X = 5/4
Finally, applying the inverse tangent and using a calculator, we will find the required measure.
m∠X = arctan (5/4) ≈ 51.3^(∘)
