Question

In ∆ABC,AB=6√3cm,AC=12cm,BC=6cm. Find measure of angle A​

Answer 1

Step-by-step explanation:

First of all, we can clearly check and verify that whether the given triangle is an right angled triangle or not.

So, by applying Pythagoras Theorem, we get :

AC² = 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°

Answer 2

Answer:

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Given:

In △ABC

• AB=6√3cm
• AC=12cm
• BC=6cm

Solution:

AC²=144

AB² =108

BC² =36

Since,

AC² =AB² +BC²

∴ By Converse of Pythagoras Theorem,

△ABC is an Right Angle Triangle at B.

∴∠B=90°

we know that

In a right angled triangle, If one side is half of the hypotenuse then the angle opposite to the that side is 30°

Here BC is Half of AC

Thus , measure of ∠A=30°