Question

If and if angle a:angle b:angle c = 1/2:1/3:1/6 calculate the measure of angle a angle b angle c

Answer 1

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Given :-

In triangle ∆ABC the angles are in a ratio ,

A : B : C = ( 1 / 2 ) : ( 1 / 3 ) : ( 1 / 6 )

To find :-

The measure of angle A , B and C.

Salutation :-

•°• A : B : C = ( 1 / 2 ) : ( 1 / 3 ) : ( 1 / 6 )

= ( 1 / 2 ) × 6 : ( 1 / 3 ) × 6 : ( 1 / 6 ) × 6

= 3 : 2 : 1

Now , let the common Ratio of the following be x.

Then , Angle A = 3x

Angle B = 2x

Angle C = x

So , 3x + 2x + x = 180°

[ ★ Sum of the angles of a triangle is 180° ]

6x = 180°

x = 180° / 6

x = 30°

•°• Angle A ( 3x ) = 3 × 30° = 90°

•°• Angle B ( 2x ) = 2 × 30° = 60°

•°• Angle C ( x ) = 30°

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Verification :-

Angle A + angle B + angle C = 180°

90° + 60° + 30° = 180°

180° = 180°

•°• R.H.S = L.H.S

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