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Answer :
At 67.38° angle of depression should the light be shown to locate the boat.
What are trigonometric ratios in terms of a right-angle triangle?
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A person in a 300-foot-tall lighthouse is attempting to locate a boat floating in the water 720 feet from the bottom of the lighthouse.
∴ In the perspective of the reference angle opposite is 720 feet and the adjacent is 300 feet and we know tan is opposite over the adjacent.
Assuming the angle of depression to be Ф.
∴ tan(Ф) = 720/300.
tanФ = 2.4
Ф = tan⁻¹(2.4).
Ф = 67.38°
learn more about inverse trig functions here :
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