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Question
In the following figure, write BC, AC, and CD in ascending order of their lengths.
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Solution
In ΔABC,
∠BAC < ∠ABC
BC < AC ....( 1 )
Now, ∠ACB = 180° - ∠ABC - ∠BAC
∠ACB = 180° - 73° - 47°
∠ACB = 60°
Now, ∠ACD = 180° - ∠ACB
∠ACD = 180° - 60° = 120°
Now, in ΔACD,
∠ADC = 180° - ∠ACD - ∠CAD
∠ADC = 180° - 120° - 31°
∠ADC = 29°
Since ∠ADC < ∠CAD, we have
AC < CD ....( 2 )
From ( 1 ) and ( 2 ), we have
BC < AC < CD.
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