The length of XY is 27.6yd
Cosine rule is important in finding the sides and angles of a triangle. It is applicable to a SAS triangle I.e. there must be presence of two sides with an angle in between them to use the rule.
To find the distance XY, we will use the cosine formula as shown:
XY² = YZ² + XZ² -2(YZ)(XZ)cosθ
Substitute the given angles and side measures in the expression above:
XY² = 19² + 15² -2(19)(15)cos108
XY² = 361 + 225 - 570cos108
XY² = 586 - (-176.14)
XY² = 762.13
XY = √762.13
XY =27.6yd
Hence the length of XY is 27.6yd
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