Allison is 5 ft tall. One afternoon her shadow measured 2.5 ft. At the same time, the shadow of her favorite tree was 14.5 ft. What is the height of the tree?

At the same time, the sun casts a shadow on the girl and tree creating two similar right triangles. You can use a ratio of girl's height to her shadow will be the same as the tree's height to it's shadow.

5 / 2.5 = T / 14.5
2 = T / 14.5
2 * 14.5 = T
29 ft = Tree

Answer Link

ap8997154 ap8997154 · Answer 2 · 2022-05-23T11:42:41+02:00

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the tree will be 29 ft.

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,

Tangent(θ) = Perpendicular/Base

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 the height of the Allison is 5ft, while the shadow it makes is 2.5 ft. Also, the shadow of the tree is 14.5 ft. therefore, the height of the tree will be,

(Height of the Allison)/(Measurement of Allison's Shadow) = (Height of the tree)/(Measurement of tree's Shadow)

5 ft/2.5ft = Height of the tree/ 14.5

Height of the tree = 29 ft

Hence, the height of the tree will be 29 ft.

Learn more about Tangent (Tanθ):

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