Question Type 1: Finding angles using bearings Exercises

In triangle $ABC$, the bearing of $AB$ is $310^\circ$, the bearing of $BC$ is $020^\circ$ and the bearing of $CA$ is $140^\circ$. Determine all three interior angles of the triangle.

A vessel sails from X to Y on a bearing of $125^\circ$ for 90 km, then to Z on a bearing of $305^\circ$ for 75 km. Determine the bearing from Z back to X.

A ship sails from $O$ to $A$ on a bearing of $070^\circ$ for $40\text{ km}$, then to $B$ on a bearing of $220^\circ$ for $60\text{ km}$. Calculate the direct distance $OB$.

In triangle $ABC$, the bearing from $A$ to $B$ is $050^\circ$ and from $B$ to $C$ is $170^\circ$. Find the interior angle $\angle ABC$.

In triangle ABC, $AB=80 \text{ m}$ and $BC=120 \text{ m}$. The bearing from A to B is $020^\circ$ and from B to C is $155^\circ$. Calculate the length $AC$.

In triangle $ABC$, $AB = 200\text{ m}$ and $BC = 180\text{ m}$. The bearing of $B$ from $A$ is $330^\circ$ and the bearing of $C$ from $B$ is $070^\circ$. Calculate the distance $AC$.

A plane travels from P to Q on bearing $055^\circ$ for 120 km, then from Q to R on bearing $200^\circ$ for 150 km. Find the distance PR.

A navigator measures the bearing $AB=078^\circ$ and $BC=248^\circ$ in triangle ABC with $AB=120\text{ km}$ and $BC=160\text{ km}$. First find angle $ABC$, then calculate $AC$.

A helicopter flies from H to J on bearing $350^\circ$ for $80 \text{ km}$, then to K on bearing $110^\circ$ for $100 \text{ km}$, then to L on bearing $220^\circ$ for $90 \text{ km}$. Calculate the straight-line distance $HL$.

A plane flies from A to B on a bearing of $045^\circ$ for $100\text{ km}$, then from B to C on a bearing of $120^\circ$ for $150\text{ km}$. Find the straight-line distance $AC$.

A point A is 140 km from B on a bearing of $110^\circ$, and B is 190 km from C on a bearing of $215^\circ$. Find the distance $AC$.

A surveyor walks from A to B on a bearing of $145^\circ$, then from B to C on a bearing of $290^\circ$. Determine the interior angle $\angle ABC$ of triangle ABC.