In a ΔABC right angled at A, if ∠ABC = 60° and AC = 4 units, then length of BC (in units) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{8}{\sqrt{3}}\)
The right angle is at A, so BC is the hypotenuse, and AC is the side opposite the 60° angle at B. The sine of an angle links these two sides.
Opposite side over hypotenuse: \(\sin B=\displaystyle\frac{AC}{BC}\)
\(\sin60^\circ=\displaystyle\frac{\sqrt{3}}{2}=\frac{4}{BC}\)
\(BC=\displaystyle\frac{8}{\sqrt{3}}\) units
