All the various parts of the question is calculated in the explanation part. This question determined by using law of sines.
We have to find the value of x.
In triangle ABC with sides a,b,c labeled in the usual way, the Law of Sines is
[tex]\bold{\dfrac{SinA}{a} =\dfrac{SinB}{b} =\dfrac{SinC}{c}}[/tex] ..........(1)
(1) Given that:
A=46, B=29, a=x, b=5,put this values in (1)
[tex]\dfrac{Sin\;46}{x} =\dfrac{Sin\;29}{5} \\\\x=7.418[/tex]
a = 7.418
(2) Given: A = 65,B = 53, put this value in (1)
[tex]\dfrac{x}{sin\;65} = \dfrac{22}{sin \; 53}[/tex]
x = 24.96
(3) Given that: A= 15, B = 128, put this value in (1)
[tex]\dfrac{x}{sin\;15} = \dfrac{12}{sin \; 128}[/tex]
x = 3.9
(4),A=73,B=59 put this value in (1)
[tex]x= 18\dfrac{sin\;73}{sin\;59}[/tex]
x = 20.1
(5) Now, find the missing angle 180-19-26=135
[tex]x= 32\dfrac{sin\;19}{sin\;135}[/tex]
x = 14.7
(6) Now, find the missing angle 180-78-75=27
[tex]x= 28\dfrac{sin\;27}{sin\;75}[/tex]
x = 13.2
(7) Now, find the missing angle 180-51-70=59
[tex]x= 9\dfrac{sin\;59}{sin\;70}[/tex]
x = 8.2
(8) Now, find the missing angle 180-52-33=95
[tex]\dfrac{x}{sin\;33} = \dfrac{16}{sin \; 95}[/tex]
x = 8.7
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