Question

if the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the
lengths of the diagonals of the rhombus.
​

Answer 1

Answer:

Given : side of rhombus = 8 cm

To find : length of diagonals

Explanation:

Here ,

∠A = 60°

∠C = 60°

now , in traingle AOB

using the trigonometric ratios

sin 30° = \frac{P}{H}

H

P

\begin{gathered}\frac{1}{2}= \frac{OB}{8} \\\\OB = 4 cm\end{gathered}

2

1

=

8

OB

OB=4cm

now , OB = OD = 4 cm

diagonal BD = 4+4 = 8 cm

similarly in triangle AOB

using the trigonometric ratios

\begin{gathered}\cos 30^\circ = \frac{B}{H}\\\\\frac{\sqrt{3} }{2}=\frac{AO}{8}\\\\AO = 4\sqrt{3}\end{gathered}

cos30

∘

=

H

B

2

3

=

8

AO

AO=4

3

THUS ,

diagonal AC = 8√3

hence , The diagonals are 8 cm and 8√3 cm

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