Use the Law of Sines to solve for all possible triangles tha

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers t Below, enter your answers so that

Solution

a = 33 ; c = 46 ; A = 34

I cannot see to how many decimal places we have to round off so, i am rounding off all answers to 1decimal place

Apply sine rule :

a/sinA = c/sinC

sinC = 46*sin34/33 = 0.779 ; C1 = 51.21 deg

C2 = 180 - 51.21 = 128.78 = 128.8 deg

B1 = 180 -A -C1 = 94.79 = 95.8 deg ; B2 = 17.2 deg

Now find b1 and b2 :

b1/sinB1 = a/sinA

b1 = sin95.8*33/sin34 = 58.71 = 58.7

b2/sinB2 = a/sinA

b2 = sin17.2*33/sin34 = 17.45 = 17.5