Question

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

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}

Explanation: