Question

if CB=12,What is the Value of AC? A
`6 √(2)`B
`12 √(2)`C
`12`D
`12 √(3)`

Answer 1

`12\sqrt[]{2}`

Step-by-step explanation:

To be able to find AC, we 1st of all need to find CD.

Using trig ratios, let's go ahead and determine what the value of CD is;

`\begin{gathered} \sin 45=(CD)/(12) \\ CD=12\sin 45 \\ \therefore CD=12\ast\frac{\sqrt[]{2}}{2}=6\sqrt[]{2} \end{gathered}`

Since we know CD, let's go ahead and find AC;

`\begin{gathered} \sin 30=\frac{6\sqrt[]{2}}{AC} \\ AC\sin 30=6\sqrt[]{2} \\ AC=\frac{6\sqrt[]{2}}{\sin 30}=\frac{6\sqrt[]{2}}{(1)/(2)}=6\sqrt[]{2}\ast(2)/(1)=12\sqrt[]{2} \end{gathered}`