sine law to find angle R
[tex]\displaystyle \frac{\sin R}{122}= \frac{\sin 64}{187.5} \\ \\
\sin R = \frac{122\sin 64}{187.5} \\ \\
R = \sin^{-1} \left[ \frac{122\sin 64}{187.5} \right] \\ \\
R \approx 35.7899447211[/tex]
All angles in triangle add to 180 so we can find angle P
P = 180 - R - Q
P = 180 - 35.7899447211 - 64
P = 80.2100552789
sine law with angle P to find length of RQ
[tex]\displaystyle
\frac{RQ}{\sin P} = \frac{187.5}{\sin 64} \\ \\
RQ = \frac{187.5\sin P}{\sin 64} \\ \\
RQ = \frac{187.5\sin 80.2100552789}{\sin 64} \\ \\
RQ = 205.57[/tex]
or use cosine law
[tex]RQ = \sqrt{187.5^2 + 122^2 - 2(187.5)(122) \cos80.2100552789} \\ RQ \approx 205.57[/tex]
either way the answer is 205.57 feet
