Question

In the adjoining figure, ΔABC is a right-angled triangle in which ∠B = 90⁰, ∠30⁰ and AC = 20cm. Find (i) BC, (ii) AB. 

Answer 1

From the given right-angled triangle, we have:

`(BC)/(AC) = sin 30^0`

⇒`(BC)/20=1/2` 

⇒BC = `20/2 = 10cm`

Also, `(AB)/(AC) = cos 30^0`

⇒`(AB)/20=sqrt(3)/2`

⇒`AB = (20xxsqrt(3)/2) = 10sqrt(3) cm`

∴ BC = 10cm and AB = 10`sqrt(3)` cm