1. In △ ABC, it is known that a = π / 3, a = √ 3, B = 1, a = 4, B = 4 √ 3, a = 30 ° solution, B = 5 √ 3, C = 15, B = 30 ° solution Why can't we get 150 degrees

1. In △ ABC, it is known that a = π / 3, a = √ 3, B = 1, a = 4, B = 4 √ 3, a = 30 ° solution, B = 5 √ 3, C = 15, B = 30 ° solution Why can't we get 150 degrees

1）
A=π/3 a=√3 b=1
According to the sine theorem a / Sina = B / SINB
√3：√3/2= 1：sinB
sinB=1/2
So B = 30 degrees (less than 150 degrees)
Because if 150 ° is taken, 150 + 60 > 180 ° will happen
The sum of the internal angles of a triangle is 180 degrees
So a = 90 degrees
c=2
2) A = 4 B = 4 √ 3 a = 30 ° solution triangle
a/sinA=b/sinB= 8
sinB=b/8=√3/2
B = 120 ° or B = 60 °
So C = 30 ° C = a = 4
Or C = 90 ° C = 8
3）b= 5√3 c=15 B=30°
b/sinB=c/sinC
5√3：1/2 =15：sinC
sinC=√3/2
C = 120 ° or C = 60 °
So a = 30 degrees or 90 degrees
If a = 30 ° then a = b = 5 √ 3
If a = 90 ° then a = 2B = 10 √ 3