The distance from point AA to point BB is calculated using trigonometric functions, specifically tangent, applied to two separate right-angled triangles formed by the horizontal distances and the constant height of the lighthouse. By solving for the lighthouse's height from point AA and then using that to find the distance of BB from the lighthouse, the distance between AA and BB can be determined by subtraction.
The distance from point AA to point BB can be calculated using trigonometry, specifically, the tangent function which relates angles to distances in right-angled triangles. We have two triangles to consider, each with the lighthouse as the top point and the points AA and BB as the base of each triangle.
Firstly, for point AA:
Using the formula tangent of the angle (tan) = opposite side / adjacent side, we can write tan(16°) = height of lighthouse / 1159 feet.
Solving for the height, we find height = 1159 feet * tan(16°).
Next, for point BB:
Now we again apply the tan function: tan(8°) = height of lighthouse / distance of BB from the lighthouse.
Since the height of the lighthouse doesn't change, we can set the two equations equal to each other to solve for the distance of BB from the lighthouse. Thus, distance of BB from lighthouse = height / tan(8°).
Subtracting the distance of AA from BB, we find the distance between AA and BB = distance of BB from lighthouse - 1159 feet.
By performing these calculations, you can find the distance between AA and BB, rounding to the nearest foot as necessary.