Question

In ∆ABC, m∠A = 60º, m∠C = 30º, and AB = 6 inches. What is the length of side BC?

Answer 1

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 $\frac{XY}{sin(Z)}=\frac{YZ}{sin(X)}=\frac{XZ}{sin(Y)}$

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

∵  $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∴ $\frac{6}{sin(30)}=\frac{BC}{sin(60)}$

- By using cross multiplication

∴ BC × sin(30) = 6 × sin(60)

∵ sin(30) = $\frac{1}{2}$  and sin(60) = $\frac{\sqrt{3}}{2}$

∴ $\frac{1}{2}$ BC = 6( $\frac{\sqrt{3}}{2}$ )

∴ $\frac{1}{2}$ BC = $3\sqrt{3}$

- 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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