The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.
What are trigonometric ratios?
The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
sec θ = hypotenuse/adjacent
cosec θ = hypotenuse/opposite
cot θ = adjacent/opposite
Calculation:
It is given that,
The height of the bacon-light is 135 feet above the water
Consider the horizontal distance between the boat and the lighthouse = x feet
The angle of elevation is given as 4°
Constructing a model as below in the figure.
From the trigonometric ratios, we have
tan θ = 135/x
⇒ tan 4° = 135/x
⇒ x = 135/tan 4°
∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)
Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.
Learn more about trigonometric ratios here:
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