Question

In the right triangle shown, mA = 30° and BC = 6√2.

Answer 1

AC=14.7

Step-by-step explanation

Step 1

given the right triangle

a)let

`\begin{gathered} angle=30 \\ opposite\text{ side=BC=6}√(2) \\ adjacent\text{ side=x} \end{gathered}`

hence , we need a trigonometric function that relates those values, it is

`tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}`

replace and solve for x(AC)

`\begin{gathered} tan\text{ 30}=(6√(2))/(x) \\ x=\frac{6√(2)}{tan\text{ 30}} \\ x=(6√(2))/((1)/(√(3)))=(6√(2)√(3))/(1) \\ x=14.6969 \\ rounded \\ x=14.7 \end{gathered}`

therefore, the answer is 14.7 ( decimal form)

I hope this helps you