Question

in a triangle ABC, AB = 6√3cm ,AC = 12cm, BC = 6 cm. find the measure of angle B

Answer 1

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⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐
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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°


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]



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Answer 2

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*⃣*⃣*⃣*⃣*⃣ ANSWER *⃣*⃣*⃣*⃣*⃣

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From the given information, it is clear that the triangle is a right angled triangle.


You can check it by applying the formula :

(Hypotenuse)² = (Height)²+(Base)²


Now, if u construct the right angled triangle accordingly, u can see <B measures 90°.


See the above picture too. So, <B = 90°.




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