Determine the number of possible solutions for a triangle with b=37 degrees, a=32, b=27

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

we have

step 1

Find the measure of angle A

substitute the values

The measure of angle A could have two measures

the first measure------->

the second measure ----->

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to  

substitute the values

step 3

Find the first length of side c

substitute the values

therefore

the measures for the first solution of the triangle are

,

,

,

step 4    

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to  

substitute the values

step 5

Find the second length of side c

substitute the values

therefore

the measures for the second solution of the triangle are

,

,

,