Question

In ΔXYZ, XY = 6.32, YZ = 5.83, and XZ = 11.05. m∠Y = º.

Answer 1

130.8 degrees

Answer 2

Answer: 130.8 degrees

Step-by-step explanation:

The problem can be solved by using the cosine theorem:

`a^2 = b^2 + c^2 - 2bc cos \alpha` (1)

where

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

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

`cos \alpha = (b^2+c^2-a^2)/(bc)=((6.32)^2+(5.83)^2-(11.05)^2)/(2(5.83)(6.32))=-0.654`

So, the angle is

`\alpha=cos^(-1)(-0.654)=130.8^(\circ)`