Math problem using triangle?

The Problem Says:



You are sailing due east (90degreeT) from the mouth of the York River across the Chesapeake Bay to Old Dominion Plantation Flats light at Cape Charles on the Eastern Shore on an exceptionally clear day. You can see Wolf Trap light due north (0 degreeT) of your present position. On your chart you measure the distance from Wolf Trap light to Old Plantation Flats light to be 13.1 nautical miles. On your chart you measure the bearing from Wolf Trap light to Old Plantation Flats light to be 140degrees T. How many nautical miles(to the nearest tenth) is it from your boat to Old Plantation Flats light? How many nautical miles (to the nearest tenth) is it from your boat to Wolf Trap light?



Please solve this problem and explain how you did it.Math problem using triangle?
You are sailing straight at plantation flats light, and at 90 degrees to you is wolf trap light.



From wolf trap light to plantation light imagine a line drawn to complete a right angle triangle between you, wolf trap and plantation light.



Measuring a bearing from wolf trap 140 degrees...you know that bearings are measured from North, in a clockwise direction....you also know that angles on a straight line = 180 so subtract 140 from 180...180 - 140 = 40...this gives you the angle at the top of the triangle.





You know the distance between wolf trap and plantation light is 13.1 miles, this is the hypotenuse (longest side) of your triangle.



Therefore, the side opposite your 40 degree angle = the distance you are away from plantation light.



use: Sin 40 = opposite/hypotenuse



Sin 40 = x/13.1....so Sin 40 * 13.1 = distance to plantation light



use: Cos 40 = adjacent/hypotenuse to find distance from you to wolf trap



Cos 40 = x/13.1



x = cos 40 * 13.1