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)`

Answer 1

From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = \[\boxed{60°}\]   ...[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 \[\boxed{\text{BC}}\] = `sqrt(3)/2` AC   ...[Side opposite to 60°]

∴ \[\boxed{\text{AB}}\] = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ \[\boxed{\text{AB}}\] = 6 and BC = `6sqrt(3)`