Question

Help pls, Hunter is 1.75 meters tall. At 12 noon, he measures the length of a tree's shadow to be 30.85 meters. He stands 26.8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer 1

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the tree is 13.33 meters.

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.

Hunter is standing 26.8 meters away from the tree while the shadow of the tree is 30.85 meters long. Since the distance between the Hunter and the top of the tree is equal to the shadow of the hunter. Therefore, the distance between Hunter and the top of the tree will be,

Distance between Hunter and the top of the tree = 30.85m - 26.8 m = 4.05 meter

Now, using the tangent function we can write,

Height of Hunter/ Shadow of hunter = Height of tree / Shadow of tree

1.75 m / 4.05 m = Height of the tree / 30.85 m

Height of the tree = 13.33 meters

Hence, the height of the tree is 13.33 meters.

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