Answer:
BC = 6√3 inches
Step-by-step explanation:
Given - A = 60°, C = 30°, and AB = 6 inches.
To find - What is the length of side BC?
Proof -
Given that ,
∠A = 60° , ∠C = 30° , AB = 6 inches
Let AC = x
By trigonometric identity, we get
cos(60°) = 6/x
⇒x = 6/cos(60°) = 12
⇒AC = 12
Now,
we have
AB = 6 inches , AC = 12 inches
By Pythagoras theorem , we get
(12)² = (6)² + (BC)²
⇒(BC)² = 144 - 36
⇒(BC)² = 108
⇒BC = √108
⇒BC = 6√3 inches
∴ we get
BC = 6√3 inches