Question

Assertion :In triangle ABC, if the sides b, c and the angle $\angle BAC$ are known, then a unique triangle can only be formed if $\sin B=\frac{b}{c}$ and $\angle B$ is acute. Reason: If $\sin B=\frac{b}{c}$ and B is acute, then $△ABC$ does not exist.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Both Assertion and Reason are incorrect.

Answer 1

The correct option is C Assertion is correct but Reason is incorrect.

If in a triangle, two sides and the internal angle between them is known, then only one unique triangle can be constructed.

So, it is not necessary that angle included has to be acute.

Even if the angle included is a right angle or an obtuse angle, we can form a unique triangle.

Hence, the reason is incorrect.
If $\sin B=\frac{b}{c}$

Applying sin rule, we get
$\sin C=1$

Now, if angle B is given to be acute, a unique triangle will exist.

Hence, the reason is incorrect.