The Laws of Sines and Cosines · Paper 1 — Free Maths AI SL Practice Questions

A surveyor measures the distance across a river. She stands at point $A$ one bank and sights a tree at point $C$ on the opposite bank. She walks $50\,\text{m}$ along the bank to point $B$. She measures $\angle BAC = 72°$ and $\angle ABC = 58°$.

In triangle $PQR$, $PQ = 9\,\text{cm}$, $PR = 7\,\text{cm}$, and $\angle QPR = 50°$.

A surveyor determines the distance across a river. She marks two points, $A$ and $B$, one bank, $50\,\text{m}$ apart. She identifies a point $C$ on the opposite bank such that $\angle BAC = 72°$ and $\angle ABC = 58°$.

A surveyor is mapping a triangular plot of land $ABC$. The side lengths are $AB = 80\,\text{m}$, $BC = 130\,\text{m}$, and $CA = 150\,\text{m}$. A straight path is to be built from vertex $B$ to a point $P$ on side $AC$ such that $BP$ is perpendicular to $AC$.