Question

1. The information in the following problem allows you to construct 1 triangle. A=30degrees, a=1m, b=2m

2. The information in the following problem allows you to construct 1 triangle. A=30degrees, a=.5m, b=2m

3. The information in the following problem allows you to construct 2 triangles, find C1 and C2. B=40degrees, a=2.2m, b=1.7m

Can someone please show me how to work out these problems. Because I have a lot of questions of this type and I want to know how to solve them.
Thank you!

Answer 1

1. I think this one is true.

I think the second one is False. I think you can make 2 triangles.

Answer 2

#1 use the law of sines
sinA/a = sinB/b
(1/2)/1 = sinB/2
sinB=1
you have a right triangle

#2
(1/2)/(1/2) = sinB/2
sinB = 2
no triangle possible

#3
sinB/b = sinA/a
sin40/1.7 = sinA/2.2
sinA = .832
A = 56.3 or 123.7 degrees
C = 180-(A+B)
plug in the two values of A to get C1 and C2