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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 = □ By theorem of 30° - Geometry

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Sum

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)`

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Solution

In ∆ABC, If ∠ABC = 90°, ∠CAB=30°

∴ ∠BCA = 60°     ......[Remaining angle of a triangle]

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

∴ BC = `1/2` AC      .....[Side opposite to 30°]

and AB = `sqrt(3)/2` AC   .....[Side opposite to 60°]

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

∴ BC = 7 and AB = `7sqrt(3)`

Concept: Property of 30°- 60°- 90° Triangle Theorem
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