construct a parallelogram ABCD where ab minus is equal to 5 cm CD is equal to 3 cm and BD is equal to 6.8 cm
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Two adjacent sides and the respective diagonal makes a triangle and here, we have the length of two sides and the angle between them..
By using cosine law,
(Refer to the attachment)
➙ d² = (4a)² + (3a)² - 2×4a×3a×cos 60°
➙ d² = 16a² + 9a² - 24a² × 1/2
➙ d² = 25a² - 12a²
➙ d² = 13a²
➙ d = √(13a²)
➙ d = a√13
➙ d ≈ 3.61 a (Ans)
One of the diagonal will have length 3.61a. Similarly you can find the length of other diagonal with the included angle as 120°.
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Explanation:
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