The captain of a ship at sea sights a lighthouse which is 260 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?
To find the distance of the ship from the base of the lighthouse, we can use trigonometry. Specifically, we can use the tangent function.
Let's denote the distance from the ship to the base of the lighthouse as "x". We want to find the value of x.
Given that the height of the lighthouse (H) is 260 feet and the angle of elevation (θ) is 21 degrees, we can set up the following trigonometric relationship:
tan(θ) = H / x
Plugging in the values we have:
tan(21) = 260 / x
Now, to find the value of x, we can rearrange the equation and solve for it. Here's how:
x = 260 / tan(21)
Calculating this expression, we find:
x ≈ 777.42 feet
Therefore, the ship is approximately 777.42 feet away from the base of the lighthouse.
Assuming a flat Earth, it is given by
H/X = tan 21 = 0.3839
where H = 260 feet and X is the distance to the lighthouse
So X = 677 feet
Too close for comfort.
The curvature of the Earth is negligible over such a short distance.