A lighthouse is 9.6 nautical miles from a ship which bears 156 degrees from the lighthouse. How far is the ship east of the lighthouse?
To solve this problem, we can use trigonometric ratios.
First, we need to draw a diagram to visualize the problem. Let's label the lighthouse as point A and the ship as point B. We know that AB = 9.6 nautical miles and angle A = 156 degrees.
Next, we can use the cosine ratio as follows:
cos A = adjacent/hypotenuse
We want to find the length of the adjacent side, which represents the distance east from the lighthouse to the ship.
cos 156 = adjacent/9.6
Solving for adjacent:
adjacent = cos 156 x 9.6
adjacent ≈ -3.89
Note that the cosine of 156 degrees is negative, which tells us that the adjacent side is in the opposite direction of the initial bearing (i.e. west). To find the distance east, we can take the absolute value of the adjacent side:
distance east = |adjacent| ≈ 3.89 nautical miles
Therefore, the ship is about 3.89 nautical miles east of the lighthouse.