1Use the Law of Sines to solve for all possible triangles th

1)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 to one decimal place. Below, enter your answers so that B₁ is smaller than B₂.)

a = 76,    b = 105,    A = 26°

B₁ =

°

B₂ =

°

C₁ =

°

C₂ =

°

c₁ =

c₂ =

2)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 to one decimal place. Below, enter you answers so that A₁ is smaller than A₂.)

b = 47,    c = 41,    C = 37°

A₁ =

°

A₂ =

°

B₁ =

°

B₂ =

°

a₁ =

a₂ =

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 to one decimal place.)

a = 104,    b = 89,    A = 136°

B =

C =

c =

Solution

1) a = 76,    b = 105,    A = 26°

a/sinA = b/sinB

sinB = 105*sin26/76 = 0.605

B1 = 37.3 deg ; B2 = 180 - 37.27 = 142.7 deg

C1 = 180 -A - B1 = 116.7deg ; C2 = 180 -A - B2 = 11.3 deg

So, B1 = 37.3 deg ; C1 = 116.7 deg ; B2 = 142.7 deg ; C2 = 11.3 deg

c/sinC = a/sinA

c1 = 154.9 ; c2 = 34

2) b = 47,    c = 41,    C = 37°

c/sinC = b/sinB

sinB = 47*sin37/41 = 0.689 ;

B1= 43.6 deg ; B2 = 180 - B1 = 136.4 deg

A1 = 180 - C - B1 = 99.4 deg ; A2 = 180 - C - B2 = 6.6 deg

a1/sinA1 = c/sinC ; a1 = sin99.4*41/sin37 = 67.2

a2 = 7.83