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.

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

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

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

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