taiwan-gsat 2020 QC

taiwan-gsat · Other · ast__math-a 6 marks Sine and Cosine Rules Heights and distances / angle of elevation problem
There is a triangular park with vertices at $O$, $A$, $B$. At vertex $O$ there is an observation tower 150 meters high. A person standing on the observation tower observes the other two vertices $A$, $B$ on the ground and the midpoint $C$ of $\overline{AB}$, measuring angles of depression of $30^{\circ}$, $60^{\circ}$, $45^{\circ}$ respectively. The area of this triangular park is (15)(16)(17)(18)$\sqrt{(19)}$ square meters. (Express as a simplified radical)
There is a triangular park with vertices at $O$, $A$, $B$. At vertex $O$ there is an observation tower 150 meters high. A person standing on the observation tower observes the other two vertices $A$, $B$ on the ground and the midpoint $C$ of $\overline{AB}$, measuring angles of depression of $30^{\circ}$, $60^{\circ}$, $45^{\circ}$ respectively. The area of this triangular park is (15)(16)(17)(18)$\sqrt{(19)}$ square meters. (Express as a simplified radical)