Tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The total height of the building is [45tan(82°) + 123] meters.
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,
Base is the adjacent smaller side of the angle θ.
As it is given that the angle between the person and the 86th floor of the Empire State Building is 82°, while the distance between the building and the person is 45 meters. Therefore, using the Tan function of the trigonometry the height of the building till the 86th floor of the building can be written as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm Tan(82^o) = \dfrac{\text{Height of the building till 86th floor}}{\text{Ditance between the building and the person}}[/tex]
[tex]\rm {\text{Ditance between the building and the person}} \times Tan(82^o) = {\text{Height of the building till 86th floor}}[/tex]
[tex]\rm {\text{Ditance between the building and the person}} = 45 \times Tan(82^o)\\\\{\text{Ditance between the building and the person}} = 45\ Tan(82^o)[/tex]
We know that the total height of the building is another 123 meters above the 86th floor, therefore, the total height of the building
[tex]\rm \text{Total height of the building} = 123 + 45\ Tan(82^o)[/tex]
Hence, the total height of the building is [45tan(82°) + 123] meters.
Learn more about Tangent (Tanθ):
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