The angle of elevation of the sun when a tree 6.25 meters tall casts a shadow 10.1 meters long is 31.75°.
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
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 that the tree's height is 6.25 meters tall and casts a shadow of 10.1 meters long. Therefore,
The angle of elevation is,
Tan(θ) = 6.25/10.1
θ = Tan⁻¹ (0.6188)
θ = 31.75°
Hence, the angle of elevation of the sun when a tree 6.25 meters tall casts a shadow 10.1 meters long is 31.75°.
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