Question

Solve the triangle. A = 46° a = 33 b = 26

Answer 1

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

Answer 2

Answer:

$B=34.5\degree$

$C=99.5\degree$

$c=45.2$

Step-by-step explanation:

We use the sine rule to obtain;

$\frac{\sin(B)}{b}=\frac{\sin(A)}{a}$

We substitute the values to obtain;

$\frac{\sin(B)}{26}=\frac{\sin(46\degree)}{33}$

We multiply through by 26 to obtain;

$\sin(B)=\frac{\sin(46\degree)}{33}\times 26$

$\sin(B)=0.5668$

$B=\sin^{-1}(0.5668)$

$B=34.5\degree$

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

$C+34.5\degree+46\degree=180\degree$

$C+80.5\degree=180\degree$

$C=180\degree-80.5\degree$

$C=99.5\degree$

We use the sine rule again to get;

$\frac{c}{\sin(99.5\degree)}=\frac{33}{\sin(46\degree)}$

$c=\frac{33}{\sin(46\degree)}\times \sin(99.5\degree)$

$c=45.2$