Find the lengths of the sides BC and AB.

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.

More Solutions:

Leave a Comment