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

`B=34.5\degree`

`C=99.5\degree`

`c=45.2`

Explanation:

We use the sine rule to obtain;

`(\sin(B))/(b)=(\sin(A))/(a)`

We substitute the values to obtain;

`(\sin(B))/(26)=(\sin(46\degree))/(33)`

We multiply through by 26 to obtain;

`\sin(B)=(\sin(46\degree))/(33)* 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;

`(c)/(\sin(99.5\degree))=(33)/(\sin(46\degree))`

`c=(33)/(\sin(46\degree))* \sin(99.5\degree)`

`c=45.2`