The Laws of Sines and Cosines · Paper 2 — Free Maths AI HL Practice Questions

A surveyor determines the width of a river. She stands at point $A$ one bank and observes a marker post at point $B$ directly opposite on the far bank, so that $\angle BAC = 90°$. She walks $50\,\text{m}$ along the bank to point $C$. From $C$, she measures $\angle BCA = 62°$. A second marker post at point $D$ is also on the far bank. From $C$, the angle $\angle DCA = 78°$. The distance $CD = 35\,\text{m}$.