The captain of a ship at sea sights a lighthouse which is 300 feet tall.
The captain measures the the angle of elevation to the top of the lighthouse to be 21∘
How far is the ship from the base of the lighthouse? ___ feet
Draw a diagram and review your basic trig functions. It should be clear that
300/x = tan21°
Now find x
To find the distance between the ship and the base of the lighthouse, we can use trigonometry and the concept of tangent.
Let's denote the distance between the ship and the base of the lighthouse as 'x'.
In this scenario, the height of the lighthouse acts as the opposite side of a right triangle, while the distance 'x' acts as the adjacent side. The angle of elevation, 21 degrees, corresponds to the angle at the ship.
We can use the tangent function to set up the equation:
tan(21°) = opposite/adjacent
tan(21°) = 300/x
To solve for 'x', we rearrange the equation:
x = 300 / tan(21°)
Calculating this using a calculator, we find:
x ≈ 826.56 feet
Therefore, the ship is approximately 826.56 feet away from the base of the lighthouse.