<u>Answer:</u>
BC= 38.22 cm
<u>Step-by-step explanation:</u>
We have, <em>∠BKD = 120° ,BK = 28 cm</em>, Draw a perpendicular from point K on BC let it intersect at point M. In right angled ΔBMK, <em>∠BKM=30° and BK = 28 cm</em>
sin30° = perpendicular/hypotenuse
⇒ <em>1/2 = BM/BK</em>
<em>⇒ 1/2 = BM/28</em>
<em>⇒ BM= 14 cm</em>
Now , In right angled ΔBMK ,
cos30° = base/hypotenuse
⇒ <em>√3/2 = MK/28</em>
<em>⇒ MK = 14√3 = 24.22 cm</em>
∵ KMCD is a square ∴ <em>MK = MC = 24.22 cm</em>
also, BC = BM + MC , putting values of BM & MC we get :
<em>BC = 14 cm + 24.22 cm</em> ⇒ <em>BC = 38.22 cm</em>