Question

A rhombus of side 20 cm has two angles of 60° each, then the possible length of the diaogonal is???
please answer this​

Answer 1

Note

• if it is a rhombus then it bisect angle and perpendicular also.

Question

A rhombus of side 20 cm has two angles of 60° each, then the possible length of the diagonal is ?

Given

• Side of rhombus is 20cm
• and has two angle of 60°

Find

• length of diagonal ?

Solution

• OB = OD
• OC = OA

NOW,

• we have to find AC and BD ( Diagonal )
• in ∆ OCD

$\sf → sin 30°=\frac{0B}{BC}$

$\sf → \frac{1}{2}=\frac{OB}{20}$

$\sf → 0B = \frac{\cancel{20}}{\cancel{2}}$

$\sf → OB = 10cm$

From above ---

• OB = OD

» BD = OB + OD

» BD = 10 + 10

» BD = 20cm.

Similarly

• in ∆ OCB

$\sf → cos 30°=\frac{OC}{BC}$ ( cos30° = √3/2 )

$\sf → \frac{\sqrt{3}}{\cancel{2}}=\frac{OC}{\cancel{20_{10}}}$

$\sf →\sqrt{3}=\frac{OC}{10}$

$\sf → OC = 10\sqrt{3}$

Form above ---

• OC = OA

» AC = OC + OA

» AC = 10√3 + 10√3

» AC = 20√3cm

Hence

• The length of diagonal are 20√3 and 20 cm
• Diagonal AC = 20√3 cm
• Diagonal BD = 20 cm