Answer:
\(6\sqrt{3}\approx 10.39\) inches.
Step-by-step explanation:
We have been given that in ∆ABC, \(m\angle A=60^{\circ}\), \(m\angle C=30^{\circ}\), and the length of segment AB is 6 inches. We are asked to find the length of side BC.
We can see from our attachment that in ∆ABC, the side BC is opposite side and side AB is the adjacent side for the angle A.
Since tangent relates the opposite side of a right triangle with hypotenuse, so we can set an equation to find the length of side BC as:
\(\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}\)
\(\text{tan}(60^{\circ})=\frac{\text{BC}}{6}\)
\(\sqrt{3}=\frac{\text{BC}}{6}\)
\(\sqrt{3}\times 6=\frac{\text{BC}}{6}\times 6\)
\(6\sqrt{3}=\text{BC}\)
\(\text{BC}\approx 10.39\)
Therefore, the length of side BC is \(6\sqrt{3}\approx 10.39\) inches.
