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Home Q & A Board Science-Related Homework Help Mathematics
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twinzmomma twinzmomma
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10 years ago
Theres a Triangle Each tip has A, B, or C near it. One side has 25 the other 21. And in one corner inside the triangle theres a 37 degree.

   Find the measure of angles B and C using the law of sines. Round to the nearest hundredth.
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-Saint--Saint-
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#1
10 years ago
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#2
10 years ago
a / SinA = b/SinB = c/SinC

where
upper case letters = Angles,
lower case letters =  there opposite triangle 'side'

Depending on weather the 37 degrees is opposite to the 25 or the 21 will determine the answer, but ill do both
===========================================================
1)
===========================================================
call 'a' 25 therefore 'A' is 37'b' = 21
so 25 / sin37 = 21 / sinB = c / SinC
25 / sin37 = 21 / sinB
cross multiply

21Sin37 = 25SinB
21Sin37 / 25 = sinB
B = ArcSine((21Sin37)/25
B= **30.366**

3 internal angles of a tryangle = 180,
therefore C = 180-37-30.066
C=**112.934**

a/SinA = c/SinC
25 / sin37 = c / sin112.934
25Sin112.934 = cSin37
c = 25Sin112.934 / Sin37
c = **38.257**

==========================================================
A = 37          a = 25
B = 30.366    b = 21
C = 112.934  c = 38.257    
===========================================================
2)
call 'a' 21 therefore 'A' is 37'b' = 25

so 21 / sin37 = 25 / sinB = c / SinC
21 / sin37 = 25 / sinB
cross multiply,
21SinB = 25Sin37
B = ArcSine((25Sin37)/21)
B = **45.762**

3 internal angles of a tryangle = 180,
therefore C = 180-45.761-37
C = **97.239**

a / SinA = c / SinC
21 / sin37 = c / Sin97.239
c = ((21Sin97.239)/Sin37)
c = **34.616**


==========================================================
A = 37        a = 21
B = 45.762  b = 25
C = 97.239  c = 34.616
===========================================================

NOTE the other resonce u have used cosine rule and didnt distinguish between your unintentional ambiguity
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