In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.
Answer :
In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°
AC = 6 cm
tan B = AC/BC
tan 60° = 6/BC
So we get
√3 = 6/BC
⇒ BC = 6/√3
= 6√3/(√3+√3)
= 6√3/3
= 2√3 cm
sin 60° = AC/AB
√3/2 = 6/AB
AB = (6×2)/√3
AB = (12×√3)/(√3×√3)
= 12√3/3
= 4√3 cm
Hence,
the lengths of the sides BC = 2√3 cm and AB = 4√3 cm.
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