Answered

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A = 60°, C = 30°, and AB = 6 inches. What is the length of side BC?

Sagot :

Answer:

BC = 6√3 inches

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

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