23. If XY = 13, XA = 4, and XZ = 26, then XB =

Question

Giovani York

Mathematics

19 March, 18:29

23. If XY = 13, XA = 4, and XZ = 26, then XB =

+2

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Le · Answer 1

It is given that in triangle XYZ, XY = 13, YZ=20, and XZ=25. Using the law of cosines, we have

CosC=/frac{a^2+b^2-c^2}{2ab}

cosZ=/frac{ (YZ) ^2 + (XZ) ^2 - (XY) ^2}{2 (YZ) (XZ) }

CosZ=/frac{ (20) ^2 + (25) ^2 - (13) ^2}{2 (20) (25) }

CosZ=/frac{400+625-169}{1000}

CosZ=/frac{856}{1000}

CosZ=0.856

Z=cos^{-1} (0.856)

Z=37.13^{/circ}