2021/071) For the triangle with angles A,B,C, the following trigonometric equality holds. $\sin^2B+\sin^2C−\sin^2A=\sin\,B\sin\,C$ Find the measure of the angle A.

Using law of sin's $\sin A = ka, \sin B= kb, \sin C = kc$

We get

$b^2+c^2 - a^2 = bc$

Or $a^2 = b^2 + c^2 + bc\cdots(1)$

By law of cos

$a^2 = b^2 + c^2 - 2bc \cos A \cdots(2)$

from (1) and (2)

$2 \cos A = - 1$ or $\cos A = \frac{-1}{2}$ or $A = 12^circ$