An attendant in a lighthouse receives a request for aid from a stalled craft located 5 miles due east of the lighthouse. The attendant contacts a second boat located 14 miles from the lighthouse on a bearing of N23degreesW. What is the distance and the bearing of the rescue boat from the stalled craft. without using law of cosine
You're on your way to the soulution.
So, as your intention,
tan(theta) = a / (x+5)
tan(theta) = 12.89 / (5.48 +5) = 1.23
theta = arctan(1.23) = 50.89 degrees
Or, maybe if you are looking for theta to the nearest drgree,
theta = 51 degrees
Hence, the bearing of the rescue boat from the stalled craft is
N 39deg W -------------answer.
By Pythagorean theorem,
d = sqrt[(12.89)^2 +(5.48 +5)^2] = 16.61 miles. -----answer.
sin(theta) = a / d
d = 12.89 / sin(50.89deg) = 16.61 miles
cos(theta) = (x +5) / d
d = (5.48 +5) / cos(50.89deg) = 16.61 miles.
thanks for the help!!:):)