Question

Write your answer in simplest radical form​

Answer 1

`a = 3√(6)`

Explanation:

θ = 30°

Opposite side length to θ = 3√2 in.

Adjacent side length = a

Apply the trigonometric ratio, TOA:

`tan(\theta) = (Opp)/(Adj)`

Plug in the known values

`tan(30) = (3√(2))/(a)`

Multiply both sides by a

`a*tan(30) = 3√(2)`

`a*(1)/(√(3)) = 3√(2)` (tan 30 = 1/√3)

Multiply both sides by the inverse of 1/√3 which is √3

`a = 3√(2)*√(3)`

`a = 3√(2*3)`

`a = 3√(6)`