Answer:
17.5 ft
Step-by-step explanation:
6.25/10 = x/28
x = 28(6.25/10)
x = 17.5 ft
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 17.5 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,
The base is the adjacent smaller side of the angle θ.
Given that George casts a 10-foot tall shadow when the tree casts a 28-foot shadow. Also, George's height is 6.25 feet. Therefore, the tan angel can be written as,
tan(θ)= George's height/George's shadow = Tree's height/Tree's shadow
George's height/George's shadow = Tree's height/Tree's shadow
6.25 feet / 10 feet = Tree's height/28 feet
Tree's height = 17.5 feet
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