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One angle of a triangle is 120° and it's opposite side 3cm . Find the diameter of its circumcircle.No need of irrelevant answers...​

Answer»

Step-by-step explanation:

Let ABCD be the GIVEN parallelogram.

DC = 6 cm and ∠ADC = 60°

Area of parallelogram ABCD = 30 cm2

Construction: Draw AE perpendicular to DC.

Area of a parallelogram = BASE × Height

⇒ 30 cm2 = 6 cm × AE

⇒ AE =

USING angle sum property in ΔAED:

∠ADE + ∠DEA + ∠EAD = 180°

⇒ 60° + 90° + ∠EAD = 180°

⇒ 150° + ∠EAD = 180°

⇒ ∠EAD = 180° − 150° = 30°

Thus, the angles of ΔAED are 30°, 60° and 90°.

Therefore, the ratio of the lengths of the sides of ΔAED is 1::2.

Thus, the length of other side of the parallelogram is cm.

Note: We can also draw the FIGURE by taking ∠ADE = 60° and AD = 6 cm.


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