ABCD is a rhombus with each side of length 20 cm- Angle ABC and ADC measure 60- each- The length of the diagonal AC is -

The correct option is B 20 cmConsider the rhombus ABCD In Triangle ABE, sin 30=AE/20 ⇒1/2=AE/20⇒ AE=10 cm We know that, diagonals of a Rhombus bisect each ot ...

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Standard IX

Mathematics

Values of Trigonometric Ratios

ABCD is a rho...

Question

ABCD is a rhombus with each side of length 20 cm. Angle ABC and ADC measure $60^{\circ}$ each. The length of the diagonal AC is :

10 cm

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20 cm

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15 cm

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None of these

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Solution

The correct option is B 20 cm
Consider the rhombus ABCD

In Triangle ABE, $s i n 30 = \frac{A E}{20} \Rightarrow \frac{1}{2} = \frac{A E}{20} \Rightarrow A E = 10 c m$

We know that, diagonals of a Rhombus bisect each other at right angles,

Hence, $A C = 2 A E \Rightarrow A C = 20 c m .$

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ABCD is a rhombus with each side of length 20 cm. Angle ABC and ADC measure 60∘ each. The length of the diagonal AC is :

The correct option is B 20 cmConsider the rhombus ABCD In Triangle ABE, sin 30=AE20 ⇒12=AE20 ⇒AE=10 cm We know that, diagonals of a Rhombus bisect each other at right angles, Hence, AC=2 AE ⇒AC=20 cm.

ABCD is a rhombus with each side of length 20 cm. Angle ABC and ADC measure $60^{\circ}$ each. The length of the diagonal AC is :

The correct option is B 20 cm
Consider the rhombus ABCD

In Triangle ABE, $s i n 30 = \frac{A E}{20} \Rightarrow \frac{1}{2} = \frac{A E}{20} \Rightarrow A E = 10 c m$

We know that, diagonals of a Rhombus bisect each other at right angles,

Hence, $A C = 2 A E \Rightarrow A C = 20 c m .$