AP EAMCET · Maths · Complex Number
\(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3\) represent the vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) of a triangle ABC respectively in the Argand plane. If \(\left|z_1-z_2\right|=\sqrt{25-12 \sqrt{3}},\left|\frac{z_1-z_3}{z_2-z_3}\right|=\frac{3}{4}\) and \(\underline{\mathrm{ACB}}=30^{\circ}\), then the area (in sq. units) of that traingle is
- A \(\frac{3}{2}\)
- B \(3\)
- C \(5\)
- D \(\frac{5}{2}\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\( AC = b, BC = a \) \( \frac{b}{a} = \frac{3}{4} \implies b = \frac{3}{4}a \) \( \text{Area} = \frac{1}{2}ab \sin(\angle ACB) = \frac{1}{2}a\left(\frac{3}{4}a\right)\sin(30^{\circ}) = \frac{3}{8}a^2 \cdot \frac{1}{2} = \frac{3}{16}a^2 \)…
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