X = 83°
Solution:
XY (x) = 17 ft
XZ (y) = 8 ft
ZY (z) = 16 ft
To find the angle X:
Using Law of cosine formula: [tex]a^{2}=b^{2}+c^{2}-2 bc \cos A[/tex]
[tex]x^{2}=y^{2}+z^{2}-2 bc \cos X[/tex]
Substitute the given values in the formula.
[tex]17^{2}=8^{2}+16^{2}-2 (8)(16) \cos X[/tex]
[tex]289=64+256-256 \cos X[/tex]
[tex]289=320-256 \cos X[/tex]
Subtract 320 on both sides of the equation, we get
[tex]-31=-256 \cos X[/tex]
Divide by –256 on both sides.
[tex]$\frac{-31}{-256}= \cos X[/tex]
[tex]$\cos ^{-1}\left(\frac{-31}{-256}\right)= X[/tex]
X = 83°
