IB Mathematics Applications & Interpretation 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.