Question

Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75°. What are the approximate length of side AC and measure of XA?OA. AC = 18.9;m A = 66.9°OB AC = 20.3; m XA = 34.8°O c. AC = 18.9;m A = 37.8°OD. AC = 20.3; m A = 58.9°ResetNext

Answer 1

The triangle described is shown below (this is not the correct triangle but we need something to help):

To find the lenght of side AC we need to use the law os cosines:

`AC^2=AB^2+BC^2-2(AB)(BC)\cos B`

In this case we have:

`\begin{gathered} AC^2=12^2+18^2-2(12)(18)\cos 75 \\ AC^2=356.19 \\ AC=\sqrt[]{356.19} \\ AC=18.9 \end{gathered}`

Now, to find angle A can use the law of sines:

`(\sin A)/(BC)=(\sin B)/(AC)`

Then:

`\begin{gathered} (\sin A)/(18)=(\sin 75)/(18.9) \\ \sin A=(18)/(18.9)\sin 75 \\ A=\sin ^(-1)((18)/(18.9)\sin 75) \\ A=66.9 \end{gathered}`

Therefore the correct answer is A.