1)Use the Law of Sines to solve for all possible triangles that satisfy the give
ID: 3426025 • Letter: 1
Question
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 =
B1 =
°
B2 =
°
C1 =
°
C2 =
°
c1 =
c2 =
Explanation / Answer
) 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
3) a = 104, b = 89, A = 136°
b/sinB = a/sinA
sinB = b*sinA/a = 0.594
B1 = 36.5 deg ; B2 = 180 - B1 = 143.5 deg
C1 = 180 - 136 - 36.5 = 7.5 deg ;C2 = 180 - 143.5 - 136 = DNE
So, B = 36.5 deg ; C = 7.5 deg
c/sinC = a/sinA
c = 19.54
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