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17 May, 14:00

If a tree casts a shadow of 25ft at the same time that a 4ft person casts a shadow of 11 1/2 ft, find the height of the tree?

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  1. 17 May, 14:05
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    8.70 ft

    Step-by-step explanation:

    We are given;

    Shadow of a tree as 25 ft Height of a person as 4ft Shadow of the person as 11.5 ft

    We are required to determine the height of the tree

    Step 1: Find the angle of elevation from the tip of the shadow to the top of the person.

    tan θ = opp/adj

    In this case; Opposite side = 4 ft

    Adjacent side = 11.5 ft

    Therefore; tan θ = (4 ft : 11.5 ft)

    tan θ = 0.3478

    θ = tan⁻¹ 0.3478

    θ = 19.18°

    Step 2: Calculate the height of the tree

    The angle of elevation from the tip of the shadow of the tree to the top of the tree will 19.18°

    Therefore;

    Opposite = Height of the tree

    Adjacent = 25 ft

    Thus;

    tan 19.18 ° = x/25 ft

    x = tan 19.18° * 25 ft

    = 0.3478 * 25 ft

    = 8.695

    = 8.70 ft

    Therefore, the height of the tree is 8.70 ft
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