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
Given AC, P = 4
∠ABC = 60º
Thus, Tan ∠B = 4/AB
(Tan 60º) (AB) = 4
AB = 4√3
\( {BC}^{2} \) = \( {AC}^{2} \) + \( {AB}^{2} \)
\( {BC}^{2} \) = \( {4}^{2} \) + (4/√3)^2 = 16 + 16/3
BC = √(64/3) = $\frac{8}{\sqrt{3}}$
The correct answer is Option (2) → $\frac{8}{\sqrt{3}}$