Answer:
C.11.52 centimeters
Step-by-step explanation:
Given,
In triangle ABC,
BC = 4 centimeters, m∠B = m∠C, and m∠A = 20°.
Since, the sum of all interior angles of a triangle is supplementary,
⇒ m∠A + m∠B + m∠C = 180°
⇒ 20° + m∠B + m∠B= 180°
⇒ 2 m∠B = 160°
⇒ m∠B = 80°,
Now, By the law of sines,
[tex]\frac{sin A}{BC}=\frac{sin B}{AC}[/tex]
By cross multiplication,
[tex]sin A\times AC = sin B\times BC[/tex]
[tex]\implies AC = \frac{sin B\times BC}{sin A}[/tex]
By substituting values,
[tex]AC=\frac{sin 80^{\circ}\times 4}{sin 20^{\circ}}=\frac{3.93923101205
}{0.34202014332
}=11.5175409663
\approx 11.52\text{ in}[/tex]
