### Bearings

**What are bearings?**

**Bearings**are a way of describing and using**directions**as**angles**- They are specifically defined for use in navigation because they give a precise
**location**and/or**direction**

**How are bearings defined?**

- There are
**three rules**which must be followed every time a bearing is defined- They are
**measured**from the**North**direction- An arrow showing the North line should be included on the diagram

- They are
**measured clockwise** - The angle is always written in
**3 figures**- If the angle is less than 100° the first digit will be a zero

- They are

**What are bearings used for?**

- Bearings questions will normally involve the use of Pythagoras or trigonometry to find missing distances (lengths) and directions (angles) within navigation questions
- You should always
**draw a diagram**

- You should always
- There may be a scale given or you may need to consider using a scale
- However normally in IB you will be using triangle calculations to find the distances

- Some questions may also involve the use of angle facts to find the missing directions
- To answer a question involving
**drawing bearings**the following steps may help:- STEP 1: Draw a diagram adding in any points and distances you have been given
- STEP 2: Draw a North line (arrow pointing vertically up) at the point you wish to measure the bearing
**from**- If you are given the bearing
**from A to B**draw the North line at**A**

- If you are given the bearing
- STEP 3: Measure the angle of the bearing given
**from the North line**in the**clockwise direction** - STEP 4:

- You will likely then need to use trigonometry to calculate the shortest distance or another given distance

#### Worked Example

The point B is 7 km from A on a bearing of 105°. The distance from B to C is 5 km and the bearing from B to C is 230°. Find the distance from A to C.

### Elevation & Depression

**What are the angles of elevation and depression?**

- If a person looks at an
**object**that is not on the same horizontal line as their eye-level they will be looking at either an angle of**elevation**or**depression**- If a person looks
**up**at an object their line of sight will be at an**angle of elevation**with the horizontal - If a person looks
**down**at an object their line of sight will be at an**angle of depression**with the horizontal

- If a person looks
- Angles of elevation and depression are measured
**from the horizontal** **Right-angled trigonometry**can be used to find an angle of elevation or depression or a missing distance- Tan is often used in real-life scenarios with angles of elevation and depression
- For example if we know the distance we are standing from a tree and the angle of elevation of the top of the tree we can use Tan to find its height
- Or if we are looking at a boat at to sea and we know our height above sea level and the angle of depression we can find how far away the boat is

#### Worked Example

A cliff is perpendicular to the sea and the top of the cliff stands 24 m above the level of the sea. The angle of depression from the cliff to a boat at sea is 35°. At a point m up the cliff is a flag marker and the angle of elevation from the boat to the flag marker is 18°.

### Constructing Diagrams

**What diagrams will I need to construct?**

- In IB you will be expected to construct diagrams based on information given
- The information will include
**compass directions, bearings, angles**- Look out for the
**plane**the diagram should be drawn in - It will either be
**horizontal**(something occurring at sea or on the ground) - Or it will be
**vertical**(Including height)

- Look out for the
- Work through the statements given in the instructions systematically

**What do I need to know?**

- Your diagrams will be sketches, they do not need to be accurate or to scale
- However the more accurate your diagram is the easier it is to work with

- Read the full set of instructions once before beginning to draw the diagram so you have a rough idea of where each object is
- Make sure you know your
**compass directions****Due east**means on a**bearing of 090°**- Draw the line directly to the right

**Due south**means on a**bearing of 180°**- Draw the line vertically downwards

**Due west**means on a**bearing of 270°**- Draw the line directly to the left

**Due north**means on a**bearing of 360° (or 000°)**- Draw the line vertically upwards

- Using the above bearings for compass directions will help you to estimate angles for other bearings on your diagram

#### Worked Example

A city at B is due east of a city at A and A is due north of a city at E. A city at C is due south of B.

The bearing from A to D is 155° and the bearing from D to C is 30°.

The distance AB = 50 km, the distances BC = CD = 30 km and the distances DE = AE = 40 km.

Draw and label a diagram to show the cities A, B, C, D and E and clearly mark the bearings and distances given.