Using the Law of Sines to find a triangle with one obtuse angle

Question

Using the Law of Sines to find a triangle with one obtuse angle if If no answer exists, enter DNE for all answers.

∠B is ___ degrees

∠C is ___ degrees

c= ___

Assume  is opposite side ,  is opposite side , and  is opposite side .

Answer 1

Hi,

∠A=48∘,a=31,b=34.If no answer exists, enter DNE for all answers.

As you know: a/sinA = b/sinB = c/sinC

31/sin48 = 34/sinB =====> after cross multiplication sinB = 0.82 after using calculator B = 54.60 or 180 - 54.60 = 125.40

your question pointed to obtuse angle so B = 125.40 and

C = 180-( 48 + 125.40) = 7.60

for finding side c use sine rule that it will be:

a/sinA = c/sinC =====> 31/sin48 = c/sin7.60 ======>c = 5.52

I hope it is useful,

Minoo

Answer 2

sin 48° / 31 = sin B / 34

0.7431 / 31 = sin B / 34

0.8151 = sin B

Determine B, then determine C.