The tangent or tanθ function of trigonometry is the ratio of its perpendicular to its base in a right triangle. The total height of the sky scrapper is 118.25 meters.
What is Tangent (Tanθ)?
The tangent or tanθ function of trigonometry is the ratio of its perpendicular to its base in a right triangle. 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.
Since the horizontal distance between Hannah's eyes and the sky scrapper is 194 meters while the angle between the eye and the top of the sky scrapper is 31°. Therefore, the vertical height of the sky scrapper from the height of Hannah's eye level, using the tangent function can be written as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\tan(31^o) = \dfrac{\text{Height of sky scrapper from eye level}}{194\ meters}\\\\\\\text{Height of sky scrapper from eye level} = 116.567\ meters[/tex]
Since the height of the eye level is 1.68 meters from the ground, therefore, the total height of the sky scrapper can be written as,
[tex]\rm \text{Total height of sky scrapper from ground}\\\\=(\text{Height of sky scrapper from eye level}) + 1.68\ meters\\\\= 116.567 + 1.68\\\\= 118.25\ meters[/tex]
Hence, the total height of the sky scrapper is 118.25 meters.
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