Question

Let $PQRS$ be a quadrilateral in a plane, where $QR =1, \angle PQR =\angle QRS =70^{\circ}, \angle PQS =15^{\circ}$ and $\angle PRS =40^{\circ}$. If $\angle RPS =\theta^{\circ}, PQ =\alpha$ and $PS =\beta$, then the interval(s) that contain(s) the value of $4 \alpha \beta \sin \theta^{\circ}$ is/are

• A. $(0, \sqrt{2})$
• B. $(1,2)$
• C. $(\sqrt{2}, 3)$
• D. $(2 \sqrt{2}, 3 \sqrt{2})$

Answer 1

Answer: (B)

$(1,2)$

Answer 2

The correct option is (B): $(1,2)$