Question

help please. show work

Answer 1

sine law to find angle R

$\displaystyle \frac{\sin R}{122}= \frac{\sin 64}{187.5} \\ \\ \sin R = \frac{122\sin 64}{187.5} \\ \\ R = \sin^{-1} \left[ \frac{122\sin 64}{187.5} \right] \\ \\ R \approx 35.7899447211$

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

$\displaystyle \frac{RQ}{\sin P} = \frac{187.5}{\sin 64} \\ \\ RQ = \frac{187.5\sin P}{\sin 64} \\ \\ RQ = \frac{187.5\sin 80.2100552789}{\sin 64} \\ \\ RQ = 205.57$

or use cosine law

$RQ = \sqrt{187.5^2 + 122^2 - 2(187.5)(122) \cos80.2100552789} \\ RQ \approx 205.57$

either way the answer is 205.57 feet