Question

In the figure shown above, $AC=6$. Calculate the length of segment $\overline{AB}$.

• A. $3$
• B. $5$
• C. $6$
• D. $7$
• E. It cannot be determined from the information given

Answer 1

Answer: (C)

$6$

Given, In a $\Delta$ ABC with sides a,b,c & angles A,B,C

$A=B=\frac{\pi }{3}$

$b=6$

Since, $\text{Sum of all angles in a triangle is}$ $\pi$

$\Rightarrow C=\pi -(A+B)=\frac{\pi }{3}$

Thus, $\Delta$ ABC is an equilateral triangle

i.e. $a=b=c$

Therefore, $c=b=6$

Hence, option (C) is correct.