Tangent is the ratio of perpendicular to the base. The distance between the base of the tree and the swing set is 18 feet.
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,
Base is the adjacent smaller side of the angle θ.
As it is given that the height of the tree is 11 feet, while the angle of depression is 31.43°, therefore, the tangent can be written as,
[tex]\rm{Tangent(31.43^o) = \dfrac{AB}{BC}[/tex]
Where BC is the length between the base of the tree and the AB is the height of the tree.
[tex]\rm Tangent(31.43^o) = \dfrac{11}{BC}\\\\BC = 17.999 \approx 18[/tex]
Hence, the distance between the base of the tree and the swing set is 18 feet.
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