In a ∆ABC, angle BAC = 30° and angle BCA = 60°. If AC = 13 cm and AB = 12 cm, then BC is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 5 cm.
Given that
In ∆ABC, angle BAC = 30° and angle BCA = 60°
The sum of interior angles of a triangle = 180º
Hence, angle ACB= = 180 - 30 - 60 = 90º
Using the Pythagorean theorem we get,
AC2 = AB2 + BC2
⇒ 169 = 144 + BC2
⇒ 25 = BC2
⇒ BC = 5 cm