Respuesta :

farahsherif
using sin rule:
a/sin A =b/sin B=c/sin c
SIN A=sin 46=0.72
THEN:sin B =(0.72*26)/33=0.57
then B= 34° 
AS the sum of triangle angles=180 
then C=180-(46+34)=100°
then c =(a*sin C)/sin A
sin C=sin 100=0.98
=(33*0.98)*0.72=45
kudzordzifrancis

Answer:

[tex]B=34.5\degree[/tex]

[tex]C=99.5\degree[/tex]

[tex]c=45.2[/tex]

Step-by-step explanation:

We use the sine rule to obtain;

[tex]\frac{\sin(B)}{b}=\frac{\sin(A)}{a}[/tex]

We substitute the values to obtain;

[tex]\frac{\sin(B)}{26}=\frac{\sin(46\degree)}{33}[/tex]

We multiply through by 26 to obtain;

[tex]\sin(B)=\frac{\sin(46\degree)}{33}\times 26[/tex]

[tex]\sin(B)=0.5668[/tex]

[tex]B=\sin^{-1}(0.5668)[/tex]

[tex]B=34.5\degree[/tex]

We now use the sum of angles in a triangle to obtain;

[tex]C+34.5\degree+46\degree=180\degree[/tex]

[tex]C+80.5\degree=180\degree[/tex]

[tex]C=180\degree-80.5\degree[/tex]

[tex]C=99.5\degree[/tex]

We use the sine rule again to get;

[tex]\frac{c}{\sin(99.5\degree)}=\frac{33}{\sin(46\degree)}[/tex]

[tex]c=\frac{33}{\sin(46\degree)}\times \sin(99.5\degree)[/tex]

[tex]c=45.2[/tex]

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