The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the tree is 14.928 feet.
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 distance between the tree and the fence is 4 feet, while the angle between the bottom of a fence and the top of a tree is 75°. Therefore, using the tangent function we can write,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\Tangent(75^o) = \dfrac{\text{Height of the tree}}{\text{Distance between the tree and the fence}}\\\\{\text{Height of the tree}}={\text{Distance between the tree and the fence}}\times Tangent(75^o) \\\\{\text{Height of the tree}} = 14.928\rm feet[/tex]
Hence, the height of the tree is 14.928 feet.
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