Question

Solve the triangle ABC with a=2,A=30,C=30​

Answer 1

Answer:

A = 30 degree

B = 120 degree

C = 30 degree

a = 2 units

b =

$b = 2 \sqrt{3}$

units

C = 2 units

Step-by-step explanation:

$by \: lami \: theorem \\ \\ \frac{2}{ \sin(30) } = \frac{b}{ \sin(b) } = \frac{c}{ \sin(30) } \\ \\ \frac{2}{ \sin(30) } = \frac{c}{ \sin(30) } \\ \\ c = 2 \\ \\ by \: angle \: sum \: property \\ \\ a + b + c = 180 \\ \\ 30 + b + 30 = 180 \\ \\ b = 180 - 60 \\ \\ b = 120 \: degrees. \\ \\ \frac{2}{ \sin(30) } = \frac{b}{ \sin(b) } \\ \\ \frac{2} { \sin(30) } = \frac{b}{ \sin(120) } \\ \\ 4 = \frac{b}{ \cos(60) } \\ \\ b = 4 \cos(60) \\ \\ b = 4 \times \frac{ \sqrt{3} }{2} \\ \\ b = 2 \sqrt{3 } \: \: \: units.$