Question Type 1: Finding angles using bearings Exercises

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

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

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

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

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

In triangle ABC, $AB=200 \text{ m}$ and $BC=180 \text{ m}$. Bearings are $AB=330^ \text{o}$ and $BC=070^ \text{o}$. Calculate $AC$.

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

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

In triangle ABC the bearings are $AB=310^\text{o}$, $BC=020^ \text{o}$ and $CA=140^\text{o}$. Determine all three interior angles of the triangle.

A navigator measures the bearing $AB=078^\text{o}$ and $BC=248^\text{o}$ 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 $350^\text{o}$ for 80 km, then to K on bearing $110^\text{o}$ for 100 km, then to L on bearing $220^\text{o}$ for 90 km. Calculate the straight‐line distance $HL$.

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