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sqdancefan

The angle with the largest measure is opposite the longest side. The longest side is 12. It is opposite angle B. The appropriate choice is ...

B. ∠B

Answer:

Option B. ∠B

Step-by-step explanation:

In this question three sides of a triangle are given as AB = 10, BC = 10, AC = 12

and we have to tell the largest angle of the triangle.

As per sine rule we know

sin A/BC = sin B/ AC = sin C/ AB

Here sin A/10 = sin C/10

⇒sin A = sin C

therefore ∠A = ∠C

(sin B)/12 = (sin C)/10

⇒ sin B/ sin C = 12/10 = 1.2 : 1

Therefore ∠B:∠C :: 1.2 : 1

similarly ∠B:∠A :: 1.2 : 1

Therefore ∠B is the largest angle.

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