In δxyz, xy = 6.32, yz = 5.83, and xz = 11.05. m∠y = º.

130.8 degrees

Explanation:

The problem can be solved by using the cosine theorem:

(1)

where

a,b,c are the lengths of the three sides of the triangle

is the angle between b and c

In this problem, we can identify a,b,c, with:

a = XZ = 11.05

b = XY = 6.32

c = YZ = 5.83

So, the angle corresponds to the angle m∠Y. Re-arranging eq.(1), we find

So, the angle is

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80