In the adjoining figure, Δ ABC is a right-angled triangle in which B = 90°, ∠ A= 30° and AC = 20 cm. Find (i) BC, (ii) AB.

Question

Philoid · Accepted Answer

Since, in a right angled triangle,

sin θ = Perpendicular / Hypotenuse ,

and cos θ = Base / Hypotenuse ,

where θ is the angle made between the hypotenuse and the base.

(i) ∴ In the given figure, sin 30° = BC/AC

⇒ 1/2 = BC/20

⇒ (1/2) × 20 = BC

⇒ BC = 10 cm

(ii) Now, In the given figure, cos 30° = AB/AC

⇒ √3/2 = AB/20

⇒ (√3/2) × 20 = AB

⇒ AB = 10√3 cm