Compass Bearings and True Bearings 1

Years

Year 9

Bearings

Compass Bearings and True Bearings

Compass Bearings and True Bearings 1

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Question 1 of 5

1. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Bearing of A from O $=$ $=$ (60) $°$ $°$
  
  $(i i)$ $(ii)$ Bearing of B from O $=$ $=$ (199) $°$ $°$
  
  $(i i i)$ $(iii)$ Bearing of C from O $=$ $=$ (328) $°$ $°$
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When solving for bearings, start from North and move clockwise.

$(i)$ $(i)$    Bearing of $A$ $A$ from $O$ $O$

Notice that when starting from North and heading to East, the two lines form a complementary angle.

Since complementary angles add up to $90 °$ $90°$ , we can simply subtract the measure of $∠ A O E$ $angle A O E$ , which is $30 °$ $30°$ , to get the bearing of $A$ $A$ from $O$ $O$ .

$90 ° - 30 °$ $90°-30°$ $=$ $=$ $60 °$ $60°$

$(i i)$ $(ii)$    Bearing of $B$ $B$ from $O$ $O$

Notice that when starting from North and heading to South, the two lines form a supplementary angle.

Since supplementary angles add up to $180 °$ $180°$ , we can simply add the measure of $∠ S O B$ $angle S O B$ , which is $19 °$ $19°$ , to get the bearing of $B$ $B$ from $O$ $O$ .

$180 ° + 19 °$ $180°+19°$ $=$ $=$ $199 °$ $199°$

$(i i i)$ $(iii)$    Bearing of $C$ $C$ from $O$ $O$

Notice that when starting from North and heading all the way back to North, it forms a revolution.

Since a revolution is equal to $360 °$ $360°$ , we can simply subtract the measure of $∠ C O N$ $angle C O N$ , which is $32 °$ $32°$ , to get the bearing of $C$ $C$ from $O$ $O$ .

$360 ° - 32 °$ $360°-32°$ $=$ $=$ $328 °$ $328°$

$(i) 60 °$ $(i) 60°$

$(i i) 199 °$ $(ii) 199°$

$(i i i) 328 °$ $(iii) 328°$
Question 2 of 5

2. Question
Find the compass bearing and true bearing of $A$ $A$ from $O$ $O$
- $(i)$ $(i)$ Compass Bearing $=$ $=$ (N) (19) $°$ $°$ (E)
  
  $(i i)$ $(ii)$ True Bearing $=$ $=$ (19) $° T$ $°T$
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To get a compass bearing, take the compass quadrant where the direction belongs to, then get the angle from the vertical line around to the required direction.

Compass Bearing Quadrants

Northwest Quadrant $= N$ $=N$ __ $W$ $W$

Northeast Quadrant $= N$ $=N$ __ $E$ $E$

Southwest Quadrant $= S$ $=S$ __ $W$ $W$

Southeast Quadrant $= S$ $=S$ __ $E$ $E$

The blank is filled with the distance of the bearing from the North-South (vertical) line

A true bearing is an angle measured clockwise from the True North around to the required direction.

$(i)$ $(i)$ $Compass Bearing$ $\text(Compass Bearing)$

Notice that line $A$ $A$ is located on the Northeast Quadrant.

Using the chart, we can write the compass bearing of $A$ $A$ from $O$ $O$ by using $N$ $N$ __ $E$ $E$ . Then get the angle that spans from the vertical line ( $N$ $N$ ) to $A$ $A$ , which is $19 °$ $19°$

Therefore, the compass bearing of $A$ $A$ from $O$ $O$ is $N 19 ° E$ $N 19° E$

$(i i)$ $(ii)$ $True Bearing$ $\text(True Bearing)$

Notice that line $A$ $A$ is $19 °$ $19°$ from the starting point, which is from the North line.

That means that the true bearing of $A$ $A$ from $O$ $O$ is simply $19 ° T$ $19°T$ .

$T$ $T$ stands for True North.

$(i)$ $(i)$ Compass Bearing $= N 19 ° E$ $= N 19° E$

$(i i)$ $(ii)$ True Bearing $= 19 ° T$ $=19°T$
Question 3 of 5

3. Question
Find the compass bearing and true bearing of $A$ $A$ from $O$ $O$
- $(i)$ $(i)$ Compass Bearing $=$ $=$ (N) (34) $°$ $°$ (W)
  
  $(i i)$ $(ii)$ True Bearing $=$ $=$ (326) $° T$ $°T$
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To get a compass bearing, take the compass quadrant where the direction belongs to, then get the angle from the vertical line around to the required direction.

Compass Bearing Quadrants

Northwest Quadrant $= N$ $=N$ __ $W$ $W$

Northeast Quadrant $= N$ $=N$ __ $E$ $E$

Southwest Quadrant $= S$ $=S$ __ $W$ $W$

Southeast Quadrant $= S$ $=S$ __ $E$ $E$

The blank is filled with the distance of the bearing from the North-South (vertical) line

A true bearing is an angle measured clockwise from the True North around to the required direction.

$(i)$ $(i)$ $Compass Bearing$ $\text(Compass Bearing)$

Notice that line $A$ $A$ is located on the Northwest Quadrant.

Using the chart, we can write the compass bearing of $A$ $A$ from $O$ $O$ by using $N$ $N$ __ $W$ $W$ . Then get the angle that spans from the vertical line ( $N$ $N$ ) to $A$ $A$ , which is $34 °$ $34°$

Therefore, the compass bearing of $A$ $A$ from $O$ $O$ is $N 34 ° W$ $N 34° W$

$(i i)$ $(ii)$ $True Bearing$ $\text(True Bearing)$

Notice that when starting from North and heading all the way back to North, it forms a revolution.

Since a revolution is equal to $360 °$ $360°$ , we can simply subtract the measure of $∠ A O N$ $angle A O N$ , which is $34 °$ $34°$ , to get the bearing of $A$ $A$ from $O$ $O$ .

Don’t forget to add $T$ $T$ to the bearing to indicate True North.

$360 ° - 34 °$ $360°-34°$ $=$ $=$ $326 ° T$ $326°T$

$(i)$ $(i)$ Compass Bearing $= N 34 ° W$ $= N 34° W$

$(i i)$ $(ii)$ True Bearing $= 326 ° T$ $=326°T$
Question 4 of 5

4. Question
Find the compass bearing and true bearing of $A$ $A$ from $O$ $O$
- $(i)$ $(i)$ Compass Bearing $=$ $=$ (N) (73) $°$ $°$ (W)
  
  $(i i)$ $(ii)$ True Bearing $=$ $=$ (287) $° T$ $°T$
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To get a compass bearing, take the compass quadrant where the direction belongs to, then get the angle from the vertical line around to the required direction.

Compass Bearing Quadrants

Northwest Quadrant $= N$ $=N$ __ $W$ $W$

Northeast Quadrant $= N$ $=N$ __ $E$ $E$

Southwest Quadrant $= S$ $=S$ __ $W$ $W$

Southeast Quadrant $= S$ $=S$ __ $E$ $E$

The blank is filled with the distance of the bearing from the North-South (vertical) line

A true bearing is an angle measured clockwise from the True North around to the required direction.

$(i)$ $(i)$ $Compass Bearing$ $\text(Compass Bearing)$

Notice that line $A$ $A$ is located on the Northwest Quadrant.

Using the chart, we can write the compass bearing of $A$ $A$ from $O$ $O$ by using $N$ $N$ __ $W$ $W$ . Then get the angle that spans from the vertical line ( $N$ $N$ ) to $A$ $A$ .

Notice that line $N$ $N$ and line $W$ $W$ form a complementary angle. Therefore, we can find the value of the angle by subtracting $17 °$ $17°$ from the value of a complementary angle, which is $90 °$ $90°$ .

$90 ° - 17 °$ $90°-17°$ $=$ $=$ $73 °$ $73°$

Therefore, the compass bearing of $A$ $A$ from $O$ $O$ is $N 73 ° W$ $N 73° W$

$(i i)$ $(ii)$ $True Bearing$ $\text(True Bearing)$

Notice that when starting from North and heading all the way back to North, it forms a revolution.

Since a revolution is equal to $360 °$ $360°$ , we can simply subtract the measure of $∠ A O N$ $angle A O N$ , which is $73 °$ $73°$ , to get the bearing of $A$ $A$ from $O$ $O$ .

Don’t forget to add $T$ $T$ to the bearing to indicate True North.

$360 ° - 73 °$ $360°-73°$ $=$ $=$ $287 ° T$ $287°T$

Alternatively, we can add the value of $3$ $3$ quadrants and $17 °$ $17°$ to get the same value.

$(3 \times 90 °) + 17 °$ $(3xx90°)+17°$ $=$ $=$ $270 ° + 17 °$ $270°+17°$

$=$ $=$ $287 ° T$ $287°T$

$(i)$ $(i)$ Compass Bearing $= N 73 ° W$ $= N 73° W$

$(i i)$ $(ii)$ True Bearing $= 287 ° T$ $=287°T$
Question 5 of 5

5. Question
Find the compass bearing and true bearing of $A$ $A$ from $O$ $O$
- $(i)$ $(i)$ Compass Bearing $=$ $=$ (S) (12) $°$ $°$ (E)
  
  $(i i)$ $(ii)$ True Bearing $=$ $=$ (168) $° T$ $°T$
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To get a compass bearing, take the compass quadrant where the direction belongs to, then get the angle from the vertical line around to the required direction.

Compass Bearing Quadrants

Northwest Quadrant $= N$ $=N$ __ $W$ $W$

Northeast Quadrant $= N$ $=N$ __ $E$ $E$

Southwest Quadrant $= S$ $=S$ __ $W$ $W$

Southeast Quadrant $= S$ $=S$ __ $E$ $E$

The blank is filled with the distance of the bearing from the North-South (vertical) line

A true bearing is an angle measured clockwise from the True North around to the required direction.

$(i)$ $(i)$ $Compass Bearing$ $\text(Compass Bearing)$

Notice that line $A$ $A$ is located on the Southeast Quadrant.

Using the chart, we can write the compass bearing of $A$ $A$ from $O$ $O$ by using $S$ $S$ __ $E$ $E$ . Then get the angle that spans from the vertical line ( $N$ $N$ ) to $A$ $A$ .

Notice that line $N$ $N$ and line $W$ $W$ form a supplementary angle. Therefore, we can find the value of the angle by subtracting $168 °$ $168°$ from the value of a supplementary angle, which is $180 °$ $180°$ .

$180 ° - 168 °$ $180°-168°$ $=$ $=$ $12 °$ $12°$

Therefore, the compass bearing of $A$ $A$ from $O$ $O$ is $S 12 ° E$ $S 12° E$

$(i i)$ $(ii)$ $True Bearing$ $\text(True Bearing)$

Starting clockwise from North, line $A$ $A$ gives us $168 °$ $168°$ .

Therefore, the true bearing of $A$ $A$ from $O$ $O$ is $168 ° T$ $168°T$

$(i)$ $(i)$ Compass Bearing $= S 12 ° E$ $= S 12° E$

$(i i)$ $(ii)$ True Bearing $= 168 ° T$ $=168°T$

Compass Bearings and True Bearings 1

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Quiz summary

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1. Question

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Fantastic!

2. Question

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Keep Going!

Compass Bearing Quadrants

3. Question

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Compass Bearing Quadrants

4. Question

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Compass Bearing Quadrants

5. Question

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Compass Bearing Quadrants

Quizzes

$(3 \times 90 °) + 17 °$ $(3xx90°)+17°$	$=$ $=$	$270 ° + 17 °$ $270°+17°$
	$=$ $=$	$287 ° T$ $287°T$