Question

Find the value of the side AC of the $△$ABC in terms of AB, whose length is $\sqrt{3}$ units.

• A. $\sin \theta$
• B. $\frac{\sin \theta }{\sqrt{3}}$
• C. $\sqrt{3}\sin \theta$
• D. $\sqrt{3}{\sin }^2\theta$

Answer 1

The correct option is C $\sqrt{3}\sin \theta$



In the given triangle, with respect to angle $\theta$, the opposite side is AC, and the adjacent side is BC.

$\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\Rightarrow \sin \theta =\frac{AC}{AB}$

$\Rightarrow \sin \theta =\frac{AC}{\sqrt{3}}$

$\therefore AC=\sqrt{3}\times \sin \theta =\sqrt{3}\sin \theta$