The captain of a freighter 8 km from the nearer of two unlaoding docks on the shore finds that the angle between the lines of sight to the two docks is 35 degrees. if the docks are 10km apart, how far is the tanker from the farther dock?

Answer 1

You can use the law of sines here, on a triangle formed by the ship and the two docks.

(sin 35)/10 = sin B/8

Use that to solve for sin B, which is the angle opposite the 8 km side of the triangle. Then solve for third angle C using

C = 180 - 35 - B

Finally, use
sin A/10 = sin C/c

c is the side length that you want.