In ∆ABC,<B=90°,<A=x°,<C=2x°and AB=12cm.Find BC?
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Answered by
0
Answer:
4√3 is the correct answer.
Answered by
5
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 .
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![](https://hi-static.z-dn.net/files/de3/df0e4d7cdcba13af9f82b64acb0e73c0.jpg)
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