Answer:
[tex]6\sqrt{3}\approx 10.39[/tex] inches.
Step-by-step explanation:
We have been given that in ∆ABC, [tex]m\angle A=60^{\circ}[/tex], [tex]m\angle C=30^{\circ}[/tex], 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:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(60^{\circ})=\frac{\text{BC}}{6}[/tex]
[tex]\sqrt{3}=\frac{\text{BC}}{6}[/tex]
[tex]\sqrt{3}\times 6=\frac{\text{BC}}{6}\times 6[/tex]
[tex]6\sqrt{3}=\text{BC}[/tex]
[tex]\text{BC}\approx 10.39[/tex]
Therefore, the length of side BC is [tex]6\sqrt{3}\approx 10.39[/tex] inches.
