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Sine and Cosine Formulae and Their Applications — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSine and Cosine Formulae and Their Applications2 Marks
Question
In a $\triangle\text{ABC},$ if $\text{a}=\sqrt{2},\text{b}=\sqrt{3}$ and $\text{c}=\sqrt{5},$ show that its area is $\frac{1}{2}\sqrt{6 }\text{ sq. units.}$
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Answer

The area of a triangle ABC is given by $\triangle=\frac{1}{2}\text{ab}\sin\text{C}$ $\cos\text{C}=\frac{\text{a}^2+\text{b}^2-\text{c}^2}{2\text{ab}}$ $=\frac{2+3-5}{2\sqrt{6}}$ $=0$ $\sin\text{C}=\sqrt{1-\cos^2\text{C}}$ $=1$ Therefore, $\triangle=\frac{1}{2}\text{ab}\sin\text{C}$ $\frac{1}{2}\sqrt{6}$

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