Question

What is the value of x

Answer 1

Based on the figure, we can see the following:

Hypothenuse length = 24 units

Angle A = 30 degrees

Side x = opposite of Angle A

Visiting the formula of the trigonometric function:

`\begin{gathered} \sin \text{ }\theta=\frac{opposite}{\text{hypothenuse}} \\ \\ \cos \theta=\frac{adjacent}{\text{hypothenuse}} \\ \\ \tan \theta=\frac{opposite}{\text{adjacent}} \end{gathered}`

From the given information: hypothenuse, angle A, and the opposite side, we can use the sin function to solve for the value of x.

`\begin{gathered} \sin \theta=\frac{opposite}{\text{hypothenuse}} \\ \\ \sin 30=(x)/(24) \\ 24\sin 30=x \\ 12=x \end{gathered}`

Therefore, the length of BC or the value of x is 12 units.