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Answer:
The height of the tree is 14.85 m
Step-by-step explanation:
The length of the shadow cast by the tree = 25 m
The length of the shadow cast by the signpost = 6 m
The height of the signpost = 3.5 m
Therefore, by similar triangles, we have;
Let θ, represent the angle formed by the line extending a line from the tip of the shadow, to the tip of the object and let x represent the height of the tree, we have
Tan(θ) = Opposite/Adjacent = Height of the object/(The length of the shadow)
∴ Tan(θ) = 3.5/6 = x/25
x = 25 × 3.5/6 = 14.58
The height of the tree = x = 14.85 m