Question

at a certain time of day, the angle of elevation of the sun is 70 degrees. to the nearest foot, find the height of a tree whose shadow is 32 feet long

Answer 1

See attachment for math work and answer.

Answer 2

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 39.1027 feet.

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,

$\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}$

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.

Tan(70°) = Height of the tree/Shadow of the tree

Tan(70°) = Height of the tree/ 32 feet

Height of the tree = 39.1027 feet

Hence, the height of the tree is 39.1027 feet.

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