Tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between points A and B is 1731 feet.
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,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
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.
As it is given that the distance between the lighthouse and point A is 639 feet, while the angle of elevation from that point is 11°. therefore, using the tan function, the height of the lighthouse,
[tex]\rm Tan(\theta) = \dfrac{Perpendicular}{Base}\\\\Tan(11^o) = \dfrac{CD}{CA}\\\\Tan(11^o) = \dfrac{CD}{639}\\\\Tan(11^o) \times 639 = CD\\\\[/tex]
As we know that CD is the height of the lighthouse, now
In Δ BCD
The tan function for the distance between the lighthouse and point B can be written as,
[tex]\rm Tan(\theta) = \dfrac{Perpendicular}{Base}\\\\Tan(3^o) = \dfrac{CD}{CA}\\\\Tan(3^o) = \dfrac{Tan(11^o) \times 639}{CA}\\\\CA = 2370\ ft.[/tex]
Hence, the distance between the lighthouse and Point B is 2370 ft.
Now, we know the distance between the lighthouse and Point A, and the distance between the lighthouse and Point B, therefore,
The Distance between Point A and B (AB) = CB - CA
= 2370 - 639
= 1731 ft.
Learn more about Tangent (Tanθ):
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