Applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.
How to Apply the Tangent Ratio?
The tangent ratio is: tan ∅ = opposite side length / adjacent side length of the right triangle.
Given the following:
Reference angle (∅) = 30 degrees.
Opposite side length = 8
Adjacent side length = x = ?
Using the tangent ratio, we have: tan 30 = 8/x
x(tan 30) = 8
Divide both sides by tan 30
x(tan 30)/tan 30 = 8/tan 30
x = 8/tan 30
x = 8/1/√3
x = 8 × √3
x = 8√3
Therefore, applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.
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