Question

In ΔABC, BC = 4 centimeters, m∠B = m∠C, and m∠A = 20°. What is AC to two decimal places?

Answer 1

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,

$\frac{sin A}{BC}=\frac{sin B}{AC}$

By cross multiplication,

$sin A\times AC = sin B\times BC$

$\implies AC = \frac{sin B\times BC}{sin A}$

By substituting values,

$AC=\frac{sin 80^{\circ}\times 4}{sin 20^{\circ}}=\frac{3.93923101205}{0.34202014332}=11.5175409663\approx 11.52\text{ in}$

Answer 2

M<A = 20°
m<B = m<C = 80°

Law of Sines , in any triangle we have
a/sin A = b/sin B = c/sin c

4/sin20 = AC/sin80 = AB/sin80

now we can solve AC

4/sin20 = AC/sin80
AC = 4 (sin80)/ sin20
AC = 4(0.98) / (0.34)
AC = 3.92 / 0.34
AC = 11.52

answer

C.11.52 centimeters