In a rectangle ABCD, AB = 20 cm, $∠ B A C = 60^{o}$ , calculate side BC and diagonals AC and BD.

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Solution

In triangle ABC AB =20 cm,

And as we know a rectangle has diagonals equal and and has all angles = 90.

So we can say in triangle ABC, $∠ B = 90^{o}$

So triangle ABC is a right angle triangle

applying trigonometry

$tan 60 equals fraction numerator C B over denominator A B end fraction square root of 3 equals fraction numerator C B over denominator 20 end fraction 20 asterisk times square root of 3 equals C B 20 square root of 3 c m equals C B a l s o space cos left parenthesis 60 right parenthesis equals fraction numerator A B over denominator A C end fraction 1 half equals fraction numerator 20 over denominator A C end fraction A C equals 2 asterisk times 20 A C equals 40 c m equals B D space a s space d i a g o n a l s space a r e space e q u a l space i n space r e c tan g l e space$

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