Answer
40.3º
Explanation
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]
For this triangle,
Angle A = ? (Isn't given)
Angle B = θ
Angle C = 67º
Side a = ? (Isn't given)
Side b = 56.3
Side c = 80.2
We are then told to find the Angle B, that is, θ
So, using the later parts of the Sine Rule
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]
Substituting the known variables, we have
[tex]\begin{gathered} \frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c} \\ \frac{\text{ Sin }\theta}{56.3}=\frac{\text{ Sin }67º}{80.2} \\ \text{ Sin }\theta=\frac{56.3\times\text{ Sin }67º}{80.2}=\frac{56.3\times0.9205}{80.2} \\ \text{ Sin }\theta\text{ = 0.6462} \\ \theta=Sin^{-1}(0.6462)=40.3º \end{gathered}[/tex]
Hope this Helps!!!
