Question

a A boat is heading towards a lighthouse, where Lillian is watching from a vertical distance of 145 feet above the water. Lillian measures an angle of depression to the boat at point A to be 10°. At some later time, Lillian takes another measurement and finds the angle of depression to the boat (now at point B) to be 68°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.​

Answer 1

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.

What is Tangent (Tanθ)?

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

$\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}$

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.

Learn more about Tangent (Tanθ):

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