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JEE Mains · Maths · STD 11 - Trigonometrical equations
The two adjacent sides of a cyclic quadrilateral are \(2\) and \(5\) and the angle between them is \(60^o\). If the area of the quadrilateral is \(4\sqrt 3 \) , then the perimeter of the quadrilateral is
- A \(12.5\)
- B \(13.2\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(C) \(12\)
Step-by-step Solution
Detailed explanation
\(\cos \theta=\frac{a^{2}+b^{2}-c^{2}}{2 a b}\) \({\mathbf{\theta}}=60^{\circ}\) \(\cos {60^\circ } = \frac{{4 + 25 - {c^2}}}{{2.2.5}}\) \(10=29-c^{2}\) \(c^{2}=19\) \(c=\sqrt{19}\) \(\cos \theta=\frac{a^{2}+b^{2}-c^{2}}{2 a b}\) \(\theta {\text{ }} = {120^\circ }\)…
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