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Question
In a rectangle ABCD, AB = 20cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.
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Solution
In ΔABC,
tan60° = `"BC"/"AB"`
⇒ BC = tan60° x AB
⇒ BC = `sqrt(3) xx 20`
⇒ BC = `20sqrt(3)"cm"`
cos60° = `"AB"/"AC"`
⇒ AC = `"AB"/"cos60°"`
⇒ AC = `(20)/(1)`
⇒ AC
= 20 x 2
= 40cm
Since diagonals of a rectangle are equal, therefore BD = AC = 40cm.
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