Question

A rhombus of side 20cm has two angles of 60degree each, find the length of the diagonals.

Answer 1

Step-by-step explanation:

ΔAOD

sin30°=AO/AD

1/2=AO/20

AO=10cm

AC=2AO=20cm

now

cos30°=OD/AD

√3/2=OD/20

OD=10√3cm

BD=2OD=20√3cm

Answer 2

SOLUTION

Consider a rhombus ABCD of side 20cm

such that angle BAD= angle BCD= 60°

We know that the diagonals of a rhombus are perpendicular bisector of each other.

Also, the diagonals AC and BD are bisectors of angle BAD and angle ABC respectively.

Also, the diagonals AC and BD are bisectors of angle BAD and angle ABC respectively.Therefore,

Also, the diagonals AC and BD are bisectors of angle BAD and angle ABC respectively.Therefore,∆AOB is a right Angled Triangle such that angle BAO = 30° angle AOB = 90°

Also, the diagonals AC and BD are bisectors of angle BAD and angle ABC respectively.Therefore,∆AOB is a right Angled Triangle such that angle BAO = 30° angle AOB = 90°and AB= 20°

=) cos angle BAO= Perpendicular/Hypotenuse= OA/AB

=) cos 30°= OA/AB

=) √3/2= OA/20

=) OA= 10√3 units

sin angle BAO = OB/AB

=) sin 30° = BO/20

=) 1/2 = BO/20

=) BO= 10units

Hence,

AC= 2AO

=) 2× 10√3

=) 20√3cm

BD= 2BO = 2× 10 = 20cm

hope it helps ✔️