Question

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

Answer 1

ABC is a 30 60 90 triangle
In such a triangle, the shortest side AB multiplied by the square root of 3 equals the length of the "medium" side CB.
6 * sq root (3) = 10.39
(Incidentally, the hypotenuse AC = short side*2 = 12)

Answer 2

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.