A lighthouse bears 40 degrees from a ship. After the ship sailed 10.8 miles on a course 130 degrees, the lighthouse bears 334.67 degrees at the ship. Find the distance from the second position of the ship to the lighthouse.

Please!!! Lend me your genius minds and help me. I have done what i have to do, but it seems i always lack one given. Please please please.

1 answer

Did you realize that the initial direction of the ship to the lighthouse and its direction of travel form a 90° angle ?
So we have a right-angled triangle.
Entering your data in my diagram, I found the angle I need to be 24.67°
and cos24.67 = 10.8/x, where x is the distance to the lighthouse
x = 10.8/cos24.67 = appr 11.88 miles