The triangle XYZ has XZ = 6, YZ = x, XY = z. The perimeter of the triangle XYZ is 16.

Express z in terms of x
and
Using the cosine rule, express z^2 in terms of x and cosZ
and
Hence, show that cosZ = 5x-16/3x

The perimeter is 6+x+z=16

Solve for z to answer part a and we see z=10-x

Using the law of cosines, we cam answer part b.

z^{2}=36+x^{2}-12xcos(Z)

Use this info to solve for part c:

(10-x)^{2}=36+x^{2}-12xcos(Z), now solve for cos(Z).