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Sum

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)`

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#### 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)`

Concept: Right-angled Triangles and Pythagoras Property

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