The measure of x is 88°.
Solution:
p = 16, q = 12 and r = 11
To find the angle of P:
Using cosine formula:
[tex]p^{2}=q^{2}+r^{2}-2qr \cos P[/tex]
[tex]16^{2}=12^{2}+11^{2}-2\times12 \times11 \cos x^\circ[/tex]
[tex]256=144+121-264 \cos x^\circ[/tex]
[tex]256=265-264 \cos x^\circ[/tex]
Subtract 265 from both sides.
[tex]-9=-264 \cos x^\circ[/tex]
Divide by -264 on both sides.
[tex]$\frac{-9}{-264} =\frac{ -264 \cos x^\circ}{-264}[/tex]
[tex]$\frac{3}{88} =\cos x^\circ[/tex]
[tex]$\cos^{-1} \frac{3}{88} =x^\circ[/tex]
88.05° = x°
88° = x°
The measure of x is 88°.
