(Q24)In △XYZ, right angle is at Y, YZ = x, and XY = 2x then determine ∠YXZ and ∠YZX.

Note: In the problem take YX = x, and XZ = 2x.

Given that △XYZ is a right angled triangle and right angle at Y, and YX = x and XZ = 2x.

By Pythagoras theorem

XZ2 = 2 + 2

()2 = ()2 + YZ2

x2 = 2 + YZ2

YZ2 = x2 - 2 = x2

YZ = √x2 = √x

Now, from the △XYZ

tan X =
XY
 =
√x

tan X = √ = tan °

∴ Angle YXZ is °.

tan Z =
=
√x
tan Z =
1
√
 = tan °

∴ Angle YZX is °.

Hence ∠YXZ and ∠YZX are ° and °.