Question

write your answer in simplest radical form​

Answer 1

Answer:

$a = 3\sqrt{6}$

Step-by-step explanation:

θ = 30°

Opposite side length to θ = 3√2 in.

Adjacent side length = a

Apply the trigonometric ratio, TOA:

$tan(\theta) = \frac{Opp}{Adj}$

Plug in the known values

$tan(30) = \frac{3\sqrt{2}}{a}$

Multiply both sides by a

$a*tan(30) = 3\sqrt{2}$

$a*\frac{1}{\sqrt{3}} = 3\sqrt{2}$ (tan 30 = 1/√3)

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

$a = 3\sqrt{2}*\sqrt{3}$

$a = 3\sqrt{2*3}$

$a = 3\sqrt{6}$