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Question
In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.
Options
`1 : sqrt(3) : 2`
`2 : sqrt(3) : 1`
`sqrt(3) : 1 : 2`
`sqrt(3) : 2 : 1`
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Solution
In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is `bbunderline(1 : sqrt(3) : 2)`.
Explanation:
Let us assume the length of the side opposite to ∠B = x.
In ΔABC, we have
sin(∠B) = sin 30° = `x/(AB)`
⇒ `1/2 = x/(AB)`
⇒ AB = 2x ...(i)
And, tan 30° = `x/(BC)`
⇒ `1/sqrt3 = x/(BC)`
⇒ BC = `sqrt3x` ...(ii)
∴ AC : BC : AB = x : x√3 : 2x
= 1 : √3 : 2
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