Question

In a rectangle ABCD, AB = 20cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.

Answer 1

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.