Thread: Solve Bearing and Time for Trig problem using two right angles

I'm not looking for answers, I simply do not know how to set up this problem.
I figured so far that I have a 45-45-90 triangle with a hypotenuse of sqrt(2) so each other side must be = 1. (since bearing of 135=45deg in triangle from your boat to ship)
After that I don't know where to go or what trig functions to use (we are currenly studying trig sum formulas if that helps). Any direction at all would be helpful!

A ship is moving due west at 8 knots. You are in a speed boat nautical miles directly southeast of the ship. (Thus your bearing as seen from the ship is 135 degrees.) You need to catch up with the ship, and you can move at a speed of 16 knots. So you take off at a bearing of degrees ______, and you reach the ship in ________ minutes.
Hint: Draw two right triangles.

Suppose t hours pass before you reach the ship. Then the meeting point is 8t miles west of the ship, so it is 1 + 8t miles west and 1 mile north of you. Also, you have traveled 16t miles. You can use the Pythagoras theorem to write a quadratic equation for t.

Thanks for the help! I figured it out using your method.

t = 9.11437827766148

and

bearing = 294.295188945365

I typed out more, and how I figgured it out, but I messed up and hit "+ Reply to Thread" instead of "Post Quick Reply" and its more than my consitutuion can bear to type it all out again.

Thanks again!