Question

In ∆ABC,<B=90°,<A=x°,<C=2x°and AB=12cm.Find BC?​

Answer 1

Answer:

4√3 is the correct answer.

Answer 2

Solution :-

Draw the figure with the given information

[ Refer to attachment ]

In ΔABC

• ∠B = 90°
• ∠A = x°
• ∠C = 2x°
• AB = 12 cm
• BC = ?

By angle sum property of the triangle

⇒ ∠A + ∠B + ∠C = 180°

⇒ x + 90 + 2x = 180

⇒ 3x + 90 = 180

⇒ 3x = 180 - 90

⇒ 3x = 90

⇒ x = 90/3

⇒ x = 30°

⇒ ∠A = 30°

Consider ΔABC

tan 30° = Opp/Adj = BC/AB

⇒ 1/√3 = BC/12

⇒ 12/√3 = BC

⇒ BC = 12/√3 = 12√3/3 = 4√3

⇒ BC = 4√3

⇒ BC = 4 * 1.732

⇒ BC = 6.928

Therefore the length of BC is 6.928 cm .