Question

Paper rectangle ABCD is folded in such a way that the fold passes through point B, and so A coincides with point H where H ∈ CD. BK is the folding line where K ∈ AD. m∠BKD = 120°. If BK = 28 cm, find BC.

Answer 1

The answer is BC = 38.22 cm.

Step-by-step explanation:

We have, ∠BKD = 120° ,BK = 28 cm, Draw a perpendicular from point K on BC let it intersect at point M.  In right angled ΔBMK, ∠BKM=30° and BK = 28 cm

sin30° = perpendicular/hypotenuse

1/2 = BM/BK

1/2 = BM/28

BM= 14 cm

Now , In right angled ΔBMK ,

cos30° = base/hypotenuse

√3/2 = MK/28

MK = 14√3 = 24.22 cm

KMCD is a square  MK = MC = 24.22 cm

also, BC = BM + MC , putting values of BM & MC we get :

BC = 14 cm + 24.22 cm

BC = 38.22 cm.