Question

SOMEONE HELP ME PLEASE!!! 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

BC= 38.22 cm

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