Question

In ∆ABC , AB = 12√3 cm, AC = 24 cm and BC = 12cm then find the measure of angle A
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Answer 1

A=90

B=C² = AB²+BC²

=> (12)² = (6√3)² + (6)²

=> 144 = 144

Thus, the above triangle is a right angled triangle with hypotenuse AC = 12 cm.

Now, here, we had taken base BC, and height AB.

Now, Sin A = BC/AC = 6/12 = 1/2.

So, Sin A = 1/2

=> Sin A = Sin 30°

=> A = 30°

Also, Sin C = AB/AC = (6√3)/12 = √3/2

So, Sin C = √3/2

=> Sin C = Sin 60°

=> C = 60°

Now, we know, <A + <B + <C = 180°

So, 30° + <B + 60° = 180°

=> <B = 180° - 90°

=> <B = 90° [REQUIRED ANSWER]

Answer 2

Answer:

AB²= 12X12X3 = 432

AC²= 24X24= 576

BC²= 12X12= 144

AB²+BC²=432+144=576

Hence Pythagoras theorem is verified.

So one angle is 90⁰.

others could be 45⁰ each