The length of the side BC is 6√3 inches
Step-by-step explanation:
Let us revise the sine rule
In Δ XYZ
- The side XY is opposite to angle Z
- The side YZ is opposite to angle X
- The side XZ is opposite to angle Y
- The sine rule is [tex]\frac{XY}{sin(Z)}=\frac{YZ}{sin(X)}=\frac{XZ}{sin(Y)}[/tex]
In Δ ABC
∵ m∠A = 60°
∵ m∠C = 30°
∵ AB = 6 inches
- By using the sine rule
∵ AB is opposite to ∠C
∵ BC is opposite to ∠A
∵ [tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]
∴ [tex]\frac{6}{sin(30)}=\frac{BC}{sin(60)}[/tex]
- By using cross multiplication
∴ BC × sin(30) = 6 × sin(60)
∵ sin(30) = [tex]\frac{1}{2}[/tex] and sin(60) = [tex]\frac{\sqrt{3}}{2}[/tex]
∴ [tex]\frac{1}{2}[/tex] BC = 6( [tex]\frac{\sqrt{3}}{2}[/tex] )
∴ [tex]\frac{1}{2}[/tex] BC = [tex]3\sqrt{3}[/tex]
- Multiply both sides by 2
∴ BC = 6√3
The length of the side BC is 6√3 inches
Learn more:
You can learn more about the triangles in brainly.com/question/1238144
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