Question

In a rectangle ABCD, AB = 20 cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.

Answer 1

SOLUTION :

Given : In a rectangle ABCD , AB = 20 cm , ∠BAC = 60°

In ∆ABC ,  

Let AC = x cm and CB = y cm

With reference to  ∠A,  

Base = AB, Hypotenuse = AC , Perpendicular = BC

cos A = base/ hypotenuse = AB/AC

cos 60° = 20/x

½ = 20/x            

x = 2 × 20                [cos 60°=1/2]

x = 40 cm  

AC = 40 cm

Similarly , BD = 40 cm

[In a rectangle, diagonals are equal in length]

Now ,

sin A = perpendicular/ hypotenuse = BC/AC

sin 60° = BC/AC

√3/2 = y/40

2y = 40√3

y = 40√3/2 = 20√3

y = 20√3 cm

BC = 20√3

Hence, side BC = 20√3 cm and diagonals AC & BD = 40 cm

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

since ABCD is a rectangle so all angle is right angle

since BAC = 60

SO BCA = 30

In triangle ABC

AB = 20cm

SO BC = 40cm

FROM PYTHAGORAS THEORM

AC = BD =100root5 cm