Question

From the diagram below, if the measure of ∠∠C = 30 °, and side BC = 6 then side AC = _____.

Answer 1

We are given some information about a triangle, and with the information that we have we can solve this in 2 ways: using the cosine of angle C, or the sine of angle A, an angle which we know measures 60° because the sum of the internal angles of a triangle must be 180°. Let's use the second one:

We know that the sine of an angle is:

`\begin{gathered} sin=\frac{opposite\text{ }side}{hypothenuse} \\ Therefore: \\ sin(60)=(6)/(AC) \\ 0.8660=(6)/(AC) \\ AC=(6)/(0.8660) \\ AC=6.92 \end{gathered}`

And by calculating 4√3 we know that it is 6.92, therefore, the correct answer is option A