In a right-angled triangle ABC, `angleB=90^(@), angleA=30^(@)` and AC = 20 cm. Determine the lengths of two sides BC and AB.

Explanation

From the right-angled triangle ABC, `cos30^(@)=(AB)/(AC)`
`or, (sqrt(3))/(2)=(AB)/(20) rArr 2AB=20sqrt(3) or, AB=(20sqrt(3))/(2)=10sqrt(3).`
Also in the triangle ABC, `sin30^(@)=(BC)/(AC) or, (1)/(2)=(BC)/(20)`
`or, 2BC=20 or, BC=(20)/(2)=10`
Hence the lengths of both BC is 10 cm and AB is `10sqrt(3)cm`.