Question

If WZ = 23 and XZ = 18, what is YZ?
pls help

Answer 1

The length of side YZ in the right triangle XYZ is determined as 14.1.

How to calculate the length of YZ?

The length of side YZ is calculated by applying Pythagoras theorem as follows:

Considering triangle WXZ;

WX² = 18² + 23²

WX² = 853 ------ (1)

Considering triangle XYZ;

XY² = YZ² + XZ²

XY² = YZ² + 18² ----- (2)

Considering triangle WXY;

XY² = WY² - WX²

XY² = (23 + YZ)² - 853 ------ (3)

Substitute (2) into (3);

YZ² + 18² = (23 + YZ)² - 853

YZ² + 324 = 529 + 46YZ + YZ² - 853

324 - 529 + 853 = 46YZ

648 = 46YZ

YZ = 648 / 46

YZ = 14.1

Answer 2

YZ = 14

Explanation:

We are told that;

WZ = 23 and XZ = 18

Now, ∠X in △XWZ which is a right angle triangle can be gotten using trigonometric ratio.

Thus;

WZ/XZ = tan θ

23/18 = tan θ

tan θ = 1.2778

θ = tan^(-1) 1.2778

θ = 51.95°

Now, the ∠X is 90° in △XWY.

Thus, in △XZY, ∠X = 90 - 51.95 = 38.05°

Again, using trigonometric ratio, we can find YZ.

Thus;

YZ/XZ = tan 38.05°

YZ = XZ tan 38.05°

YZ = 18 × 0.7827

YZ = 14.0886

Approximating to a whole number gives: YZ = 14