In a ΔABC right-angled at B, if AB = 4 cm and ∠C = 60°, then the length of AC is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{8\sqrt{3}}{3}\) cm
In a right triangle, sine of an angle = opposite side ÷ hypotenuse. AB is the side opposite ∠C, and AC, opposite the right angle at B, is the hypotenuse.
\(\displaystyle \sin60^\circ=\frac{AB}{AC}\)
\(\displaystyle \frac{\sqrt3}{2}=\frac{4}{AC}\)
\(\displaystyle AC=\frac{8}{\sqrt3}=\frac{8\sqrt3}{3}\) cm