Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises - Page 305: 35

The distance between $X$ and $Z$ is 664 m.

We can use the law of sines to find the distance $y$, which is the distance between $X$ and $Z$: $\frac{y}{sin~Y} = \frac{z}{sin~Z}$ $y = \frac{z~sin~Y}{sin~Z}$ $y = \frac{(960~m)~sin~(43^{\circ}30')}{sin~(95^{\circ}30')}$ $y = 664~m$ The distance between $X$ and $Z$ is 664 m.