Question

A yacht leaves port and sails 50km due east. It then changes direction and sails another 50km on bearing of 200 degrees. How far from the port is the yacht now?

Answer 1

According the low of cosines, c^2 = a^2 + b^2 - 2*a*b*cos (gamma);
let a = b = 50 miles and gamma = 200 degrees.


c^2 = 50^2 + 50^2 - 2*50*50*cos 200 = 2500 + 2500 - 5000* (- sin 70) = 5000*(1+sin 70) ~ 5000*1.9397 ~ 9698.4631
c = 98.4808