Jamal draws triangle xyz. if angle x=46 degrees, xz = 10 degrees, and yz=8 degrees, what is the approximate length of xy?

In triangle XYZ,
angle X=46 degrees,
XZ = 10 units and
YZ=8 units.

We will find the length of XY using cosine rule:

According to cosine rule:

a² = b² + c² - 2bc cosA (the figure is attached)
Here, A = 46 degree.
a = 8 units.
b = ?
c = 10 units.
⇒  b² = c² - a² -2bc cosA
⇒  b² = 100 - 64 - 160*cos(46)
⇒  b² = 100 - 64 - 160*0.69
⇒  b² = 100 - 64 - 110.4
⇒  b² = 100 - 64 - 110.4
⇒ b² = 74.4
or b = 8.62 units.
or b = 8 untis approximately.