A lighthouse operates point B 25 m above sea level sites a sailboat at point S the angle of depression of the siding is 10° how far is the boat from the base of the lighthouse give your answer to the nearest 10 m
In the given scenario, we have a right-angled triangle formed by the lighthouse (point B), the sailboat (point S), and the base of the lighthouse. The angle of depression is the angle formed between the line of sight from the lighthouse to the boat and a horizontal line.
Let's assume that the distance between the boat and the base of the lighthouse is x meters.
In a right-angled triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the tangent of the angle of depression is equal to the height of the lighthouse (25 m) divided by the distance between the boat and the base of the lighthouse (x m). So, we have:
tan(10°) = 25/x
To find x, we rearrange the equation and solve for x:
x = 25 / tan(10°)
Using a calculator, we find that tan(10°) ≈ 0.176327, so:
x ≈ 25 / 0.176327
x ≈ 141.749
Therefore, the boat is approximately 142 meters away from the base of the lighthouse.