Solve the triangle ABC, if the triangle exists. B-3554, a=39.5 b=35.3 m2A·AT-101
ID: 3026938 • Letter: S
Question
Solve the triangle ABC, if the triangle exists. B-3554, a=39.5 b=35.3 m2A·AT-101, m2c=[104-05 , m2104°105 The length of side c 58 . (Simplify your answer. Round to the nearest(Round to the nearest tenth as degree as needed. Round to the nearest minute needed.) as needed.) The measurements for the solution with the shorter side c are as follows m2A+, m2c-, (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed ) The length of side c- (Round to the nearest tenth as needed.)Explanation / Answer
We have given <B=35054',a=39.5,b=35.3
Let A,B,C are the angles of the triangles and a is the length of the side opposite angle A
b is the length of the side opposite angle B and c is the length of the side opposite angle C
60 minutes=1 degree
54 minutes =54/60 degrees =0.9 degrees
<B=35054'=35.9 degrees
By the Law of sines sinB/b=sinA/a
sinA=a*(sinB/b)=39.5*(sin(35.9)/35.3)=0.6561390394
A=arcsin(0.6561390394)=41.0060745 degrees
A=41.0060745 or A=138.9939255 degrees
the sum of the triangle is 180 degrees
if A=41.0060745 degrees C=180-(B+A)=180-(35.9+41.0060745)=103.0939255 degrees
sinB/b=sinC/c implies c=b(sinC/sin(B))=c=35.3*(sin(103.0939255 degrees)/sin(35.9 degrees))=58.6354375353
if A=138.9939255 degrees C=180-(B+A)=180-(35.9+138.9939255)=5.1060745 degrees
sinB/b=sinC/c implies c=b(sinC/sin(B))=c=35.3*(sin(5.1060745 degrees)/sin(35.9 degrees))=5.35785208189
There are two possible solutions for triangle ABC
solution 1:
<A=41.00607450,<B=35.90,<C=103.09392550
<A=41001',<B=35054',<C=10305'
a=39.5,b=35.3 ,c=58.6
solution 2:
<A=138.99392550,<B=35.90,<C=5.10607450
<A=1390,<B=35054',<C=506'
a=39.5,b=35.3 ,c=5.4
the measurements for the solution with shorter side c are as followed
<A=1390,<B=35054',<C=506' and sides a=39.5,b=35.3 ,c=5.4