# Bearings and direction word problems

0/1
##### Introduction
###### Lessons
1. Introduction to Bearings and Direction Word Problems
0/8
##### Examples
###### Lessons
1. Evaluate A Bearings Word Problem Using Trigonometric Ratios

Charlie leaves home for a bike ride, heading 040°T for 5km.

1. How far north or south is Charlie from its starting point?
2. How far east or west is Charlie from its starting point?
2. Solve A Bearings Word Problem Using the Law of Cosine

A camping group made a return journey from their base camp. From the camp, they first travelled 120°T for 3km. Then they travelled 210°T for 9km. Determine the direction and distance they need to travel if they want to return to the base camp now.

1. Analyze A Bearings Word Problem Using Trigonometric Ratios and the Law of Cosine

Melody and April go to the same school. Melody's home is 3.5km with a bearing of S16°W from school whilst April's home is 2.4km with a bearing of N42°E from school. How far away are their homes from each other?

1. Triangulate the Location of an Earthquake

Radar X detected an earthquake N55°E of it. 16km due east of Radar X, Radar Y detected the same earthquake N14°W of it.

1. Determine the earthquake from Radar X and Y.
2. Which Radar is closer to the earthquake?
2. Estimate the Height of an Object

A plane is sighted by Tom and Mary at bearings 028°T and 012°T respectively. If they are 2km away from each other, how high is the plane?

1. Applying Law of Sine and Law of Cosine

Consider the following diagram.

Find the distance between P and Q.

###### Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
• #### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
• #### Make Use of Our Learning Aids

###### Practice Accuracy

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
• #### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
###### Topic Notes

Theorems that are useful:

Pythagorean Theorem: $a^{2} + b^{2} = c^{2}$

Trig ratio: $\sin \theta = \frac{O}{H}$

$\cos \theta = \frac{A}{H}$

$\tan \theta = \frac{O}{A}$

Law of sine: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Law of cosine: $c^{2} = a^{2} + b^{2} - 2ab \cos C$