the Angle of Elevation From a Ship to the Top of a Lighthouse on the Shore is 18 Degrees. If the Light House is 20 Meters Tall and at Sea Level How Far is the Ship From the Shore to the Nearest Meter..
tan(x)=opposite over hypotenuse
x=18°
opposite=20m
tan(18°)=20m/hypotenuse
hypotenuse = 20m/tan(18°)
Can you take it from here?
To find the distance from the ship to the shore, we can use trigonometry and the given angle of elevation.
Let's refer to the height of the lighthouse (20 meters) as "h" and the distance from the ship to the shore as "d".
In a right triangle formed by the ship, the lighthouse, and the line connecting them, the angle of elevation (18 degrees) is the angle between the horizontal ground and the line of sight from the ship to the top of the lighthouse.
Using trigonometry, we can use the tangent function to find the value of the ratio of the height of the lighthouse to the distance of the ship from the shore:
tan(angle of elevation) = opposite/adjacent
tan(18 degrees) = h/d
Now, we can solve for d:
d = h / tan(angle of elevation)
d = 20 / tan(18 degrees)
Using a calculator, we find:
d ≈ 65.47 meters
Therefore, the ship is approximately 65 meters from the shore.