Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Question:

Answer each of the following questions in one word or one sentence or as per exact requirement of the question.

Find the area of the triangle $\triangle \mathrm{ABC}$ in which $a=1, b=2$ and $\angle C=60^{\circ}$.

Solution:

In $\triangle \mathrm{ABC}, a=1, b=2$ and $\angle C=60^{\circ}$.

∴ Area of the ∆ABC

$=\frac{1}{2} a b \sin C$

$=\frac{1}{2} \times 1 \times 2 \times \sin 60^{\circ}$

$=\frac{1}{2} \times 2 \times \frac{\sqrt{3}}{2}$

$=\frac{\sqrt{3}}{2}$ square units

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