Question

In the following figure, write BC, AC, and CD in ascending order of their lengths.

Answer 1

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.