To find the distance between a point $X$ and an inaccessible point $Z$, a line segment $X Y$ is constructed. Measurements show that $X Y=962 \mathrm{~m}$, angle $X Y Z=35^{\circ} 0^{\prime}$, and angle $Y Z X=117^{\circ} 54^{\prime}$. Find the distance between $X$ and $Z$ to the nearest meter. The distance between $\mathrm{X}$ and $\mathrm{Z}$ is $\mathrm{m}$. (Do not round until the final answer. Then round to the nearest meter as needed

Step 1 ：We are given that the length of line segment XY is 962 meters, the angle XYZ is 35 degrees, and the angle YZX is 117.9 degrees.

Step 2 ：We can use the Law of Sines to find the length of line segment XZ. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Step 3 ：Setting up the equation using the Law of Sines, we get \(\frac{XZ}{\sin(Y)} = \frac{XY}{\sin(Z)}\).

Step 4 ：Substituting the given values into the equation, we get \(\frac{XZ}{\sin(35)} = \frac{962}{\sin(117.9)}\).

Step 5 ：Solving for XZ, we get \(XZ = \frac{962 \times \sin(35)}{\sin(117.9)}\).

Step 6 ：Calculating the above expression, we get XZ approximately equal to 1482.2480183355817.

Step 7 ：Rounding to the nearest meter, we get XZ approximately equal to 1482 meters.

Step 8 ：Final Answer: The distance between point X and point Z is \(\boxed{1482}\) meters.