a lighthouse is 30m high. the angle of elevation from a ship to the top of the tower is 17 degrees. what is the horizontal distance from the ship to the lighthouse?
Tan17 = 30/d, d = ?
To find the horizontal distance from the ship to the lighthouse, we can use the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the angle of elevation is 17 degrees and the opposite side is the height of the lighthouse (30m). We want to find the length of the adjacent side, which is the horizontal distance from the ship to the lighthouse.
Let's denote the horizontal distance as x.
Using the tangent function, we have:
tan(17 degrees) = 30m / x
To find x, we can rearrange the equation as follows:
x = 30m / tan(17 degrees)
Now, let's calculate the value of x using a scientific calculator.
Using a calculator, we find:
tan(17 degrees) ≈ 0.305
So, the horizontal distance from the ship to the lighthouse is:
x ≈ 30m / 0.305 ≈ 98.36m
Therefore, the horizontal distance from the ship to the lighthouse is approximately 98.36 meters.