Question

Help please. show work

Answer 1

sine law to find angle R


`\displaystyle (\sin R)/(122)= (\sin 64)/(187.5) \\ \\ \sin R = (122\sin 64)/(187.5) \\ \\ R = \sin^(-1) \left[ (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 (RQ)/(\sin P) = (187.5)/(\sin 64) \\ \\ RQ = (187.5\sin P)/(\sin 64) \\ \\ RQ = (187.5\sin 80.2100552789)/(\sin 64) \\ \\ RQ = 205.57`

or use cosine law


`RQ = √(187.5^2 + 122^2 - 2(187.5)(122) \cos80.2100552789) \\ RQ \approx 205.57`

either way the answer is 205.57 feet