Question

 

Using the Law of Sines to find a triangle with one obtuse angle if ∠A=48∘,a=31,b=34. If no answer exists, enter DNE for all answers.

 

∠B is ___ degrees

 

∠C is ___ degrees

 

c= ___

 

Assume ∠A is opposite side a, ∠B is opposite side b, and ∠C is opposite side c.

Answer 1

∠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

Given below