Final answer:
We can determine the horizontal distance between the lighthouse and the boat by using the tangent function and the given information on the height of the lighthouse and the angle of depression. The horizontal distance is approximately 731.71 m.
Step-by-step explanation:
In this question, we are given the height of a lighthouse (120 m) and the angle of depression to a boat adrift in the sea (9.4 degrees). By understanding the concept of angles of depression, we can determine the horizontal distance between the lighthouse and the boat.
We can use the tangent function to find this distance. The formula is tan(angle) = opposite/adjacent. In this case, the opposite is the height of the lighthouse (120 m) and the angle is the angle of depression (9.4 degrees). By rearranging the formula, we can solve for the adjacent side, which represents the horizontal distance between the lighthouse and the boat.
Let's substitute the values into the formula: tan(9.4) = 120/adjacent.
We can rearrange the formula as adjacent = 120/tan(9.4).
Using a calculator, we can find that tan(9.4) is approximately 0.164. Plugging this value into the formula, we get adjacent = 120/0.164. Solving for adjacent, we find that the horizontal distance between the lighthouse and the boat is approximately 731.71 m.