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Question
From given figure, In ∆ABC, If AC = 12 cm. then AB =?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
Solution
From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = 60° ......[Remaining angle of a triangle]
∴ ∆ABC is 30° – 60° – 90° triangle.
∴ In ∆ABC,
by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC .......[Side opposite to 30°]
and BC = `sqrt(3)/2` AC .......[Side opposite to 60°]
∴ AB = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ AB = 6 and BC = `6sqrt(3)`
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