Question

From given figure, In ∆ABC, If ∠ABC = 90° ∠CAB = 30°, AC = 14 then for finding value of AB and BC, complete the following activity.

Activity: In ∆ABC, If ∠ABC = 90°, ∠CAB = 30°

∴ ∠BCA = `square`

By theorem of 30° – 60° – 90° triangle,

∴ `square = 1/2` AC and `square = sqrt(3)/2` AC

∴ BC = `1/2 xx square` and AB = `sqrt(3)/2 xx 14`

∴ BC = 7 and AB = `7sqrt(3)`

Answer 1

In ∆ABC, If ∠ABC = 90°, ∠CAB = 30°

∴ ∠BCA = \[\boxed{60°}\]   ...[Remaining angle of a triangle]

By theorem of 30° – 60° – 90° triangle,

∴ \[\boxed{\text{BC}}\] = `1/2` AC   ...[Side opposite to 30°]

And \[\boxed{\text{AB}}\] = `sqrt(3)/2` AC   ...[Side opposite to 60°]

∴ BC = \[\frac{1}{{2}}\times\boxed{14}\] and AB = `sqrt(3)/2 xx 14`

∴ BC = 7 and AB = `7sqrt(3)`