Solve the triangle using law of sines. If no triangle is formed, state so. Round answers to the nearest hundredth.

Question

1. 

     A=33 degrees, a=20,b=13

 

 

2.

    C=137degrees, a=19,c=8

Answer 1

law of sines:

a / sinA = b / sinB = c / sinC

 

#1:

using value for A, a, find B:

20 / sin 33 = 13 / sinB

 

sinB = 13*sin33 / 20 = 0.36

B = 21 degrees

sum of angles must be 180, C = 180 -(A+B) = 180-54 = 126

 

Looks like a legal triangle---use the basic formula to find c

 

#2:

solve for A:

c / sinC = a / sinA

8 / 0.68 = 19 / sinA

sinA = 19 * 0.68 / 8 = 1.615

Not a legal triangle---sin of angle cannot exceed 1

Answer 2

Law of Sines:

 

sin(A)/a = sin(B)/b = sin(C)/c

 

1.  A=33 degrees, a=20, b=13

 

sin(A)/a = sin(33^o)/20 = 0.027

 

Find B:

sin(A)/a = sin(B)/b

0.027 = sin(B)/13

13*(0.027) = sin(B)

0.354 = sin(B)

sin-1(0.354) = B

20.73^o = B

 

Find C and c:

C = 180^o - (33^o+20.73^o) = 126.27^o

0.027 = sin(C)/c

c = sin(126.27)/0.027

c = 29.86

 

A = 33^o, b = 20.7^o, C = 126.27^o

a = 20, b = 13, c = 29.86

 

2.  C=137degrees, a=19,c=8

 

sin(C)/c = sin(137^o)/8 = 0.085

 

Find B:

 

0.085 = sin(B)/b = sin(B)/13

13*(0.085) = sin(B)

1.105 = sin(B)

 

sin(B) cannot be greater than 1, so NO TRIANGLE CAN BE FORMED