The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance from point A to point B is 763.752ft.
<h3>What is Tangent (Tanθ)?</h3>The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
A.) The distance between the boat and the lighthouse when the angle of depression is 10°.
Tan(10°) = Height of lighthouse/ distance between the boat and the lighthouse
Distance between the boat and the lighthouse
= 145/Tan(10°) = 822.336ft
B.) The distance between the boat and the lighthouse when the angle of depression is 68°.
Tan(68°) = Height of lighthouse/ distance between the boat and the lighthouse
Distance between the boat and the lighthouse
= 145/Tan(68°) = 58.584ft
The distance between point A and B = 822.336ft - 58.584ft = 763.752 ft
Hence, the distance from point A to point B is 763.752ft.
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