Mathematics

Mathematics

Problem

In the construction of an ellipse using concentric circles of radii 4 cm4\,\text{cm} and 6 cm6\,\text{cm}, a radial line is drawn at an angle θ\theta from the center. A vertical line is drawn from the intersection of the radial line with the outer circle, and a horizontal line is drawn from the intersection with the inner circle. These lines meet at point PP. If the area of the rectangle formed by PP, its projection on the xx -axis, the origin, and its projection on the yy -axis is 63 cm26\sqrt{3}\,\text{cm}^{2}, find the possible values of the angle θ\theta (where 0<θ<90∘0 < \theta < 90^{\circ}).

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