Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 321: 40

XY has a length of 95.3 m

We can use the law of cosines to find the length $XY$: $XY^2 = XZ^2+YZ^2-2(XZ)(YZ)~cos~Z$ $XY = \sqrt{XZ^2+YZ^2-2(XZ)(YZ)~cos~Z}$ $XY = \sqrt{(153~m)^2+(103~m)^2-(2)(153~m)(103~m)~cos~37.7^{\circ}}$ $XY = \sqrt{9080.2~m^2}$ $XY = 95.3~m$ XY has a length of 95.3 m