Question

What are the angle measures of triangle ABC?

Answer 1

∠A = 90°, ∠B = 60° and ∠C = 30°

Step-by-step explanation:

• Step 1: Find whether the triangle is a right angled triangle by using Pythagoras theorem. Given sides are a = 24 (opposite to ∠A), b = 12√3 (opposite to ∠B) and c = 12 (opposite to ∠C).

⇒ 12² + (12√3)² = 144 + 432 = 576

⇒ √576 = 24 = a.  This shows that the triangle is a right angled triangle.

So ∠A = 90°

• Step 2: Use trigonometric equations to determine the other angles.

⇒ cos B = AB/BC = 12/24 = 1/2

⇒ ∠B = 60°

• Step 3: The sum of the angles in a triangle is 180°. To find ∠C,

⇒ ∠C = 180° - (90° + 60°) = 180° - 150°

⇒ ∠C = 30°