State the equivalent true bearing of the following compass bearings:
Northeast
Southeast
Southwest
Northwest
West-Northwest
South-Southeast
Consider the points P, A, and N on the following diagrams where N is the point due north of A. Find the true bearing of P from A.
Consider the points P, M, and S on the diagram, where S is the point due south of M. Find the true bearing of P from M.
Given the diagram shown, if the bearing of the clearing from the town is a \degree, find a to the nearest degree.
Consider the following diagram:
State the true bearing of point C from point B.
State the true bearing of point A from point B.
State the true bearing of point C from point A.
Draw diagrams to show the following:
The point P with a compass figure bearing of 296\degree \text{T} to point P from the origin O.
The point P with a compass figure bearing of 244 \degree \text{T} to point P from the origin O.
A bearing in the direction of \text{WNW}.
The point P with a compass bearing between \text{N} and \text{W} from the point O.
For each of the following bearings, state:
The true bearing of point A from O.
The compass bearing of point A from O.
Find the true bearing of point A from the origin O if A has a compass bearing of:
The compass bearing from A to B is \\ \text{N} 42 \degree \text{E}, while the compass bearing from C to B is \text{N} 29 \degree \text{W}.
Complete the diagram by marking it with all known information.
Find the size of \angle ABC.
Consider the following diagram:
State the compass bearing of point B from point A.
State the compass bearing of point C from point B.
State the compass bearing of point A from point C.
In the figure below, point B is due East of point A:
Calculate the true bearing of point A from point C.
State the compass bearing of point A from point C.
Consider the following diagram:
State the true bearing of point B from point C.
State the compass bearing of point B from point C.
Consider the following diagram:
State the true bearing of point C from point A.
State the compass bearing of point C from point A.
Consider the following diagram:
State the true bearing of point C from point B.
State the compass bearing of point C from point B.
If a person walks on a compass bearing of \text{SE}, and then turns around to go back in the direction they came, what direction are they heading now?
A plane travels \text{N } 36 \degree \text{W} for 9 \text{ km}, then changes direction to \text{S } 30 \degree \text{W} for 4 \text{ km} and then changes one last time to \text{S } 49 \degree \text{E} for 7 \text{ km}.
Draw a diagram to represent this journey.
A plane travels \text{N } 40 \degree \text{E} for 9 \text{ km}, then changes direction to \text{S } 34 \degree \text{E} for 4 \text{ km} and then changes one last time to \text{S } 47 \degree \text{W} for 7 \text{ km}.
Draw a diagram to represent this journey.
A man drives 14 km due east, and then 14 km due north. What is the compass bearing of his final position?
During a group hike, a hiker walked 6 \text{ km NE} of base camp. In the evening, the hiker was separated from the group and after a night lost in the wilderness, the hiker was found 6 \text{ km NW} of the base camp.
What compass bearing did the hiker follow during the night?
A commercial passenger plane flies 1801 \text{ km} on a bearing of 339 \degree from Sydney \left(S\right) to Albury \left(A\right). A second smaller plane leaves Sydney on a bearing of 249 \degree and loses radio contact at location C after flying for 1301 \text{ km}.
Find the size of \angle ASC.
Find AC, the distance the passenger plane must fly to reach point C, to the nearest\text{ km}.
Find the value of x to the nearest degree.
Find the bearing that the passenger plane must fly from point A to reach the smaller plane at point C.
Christa and James set off for a walk. They leave Point R and walk on bearing of 101 \degree for 4 \text{ km} to Point B. Christa then stops to rest but James continues walking on a bearing of 191 \degree for 2 \text{ km} to Point C.
Find \angle ABC.
Find x, to the nearest degree.
Hence, find the bearing of A from C, to the nearest degree.
A boat traveled due south for 2 \text{ km}, and then due east for 3 \text{ km}, as shown in the diagram:
Given that the angle of the compass bearing is a \degree, write the compass bearing of the boat from its starting point in terms of a \degree.
Find the value of a. Round your answer to the nearest degree.
At a point during a flight, a plane is 42 \text{ km} south and 57 \text{ km} west of the airport in Sydney that it left from:
Find the size of the angle marked b to one decimal place.
Hence, find the compass bearing of the plane from the airport.
A ship, S, is 80 kilometres from point P, on a true bearing of 0 51 \degree.
The position of the ship can also be given by its \left(x, y\right) coordinates.
Find the x-coordinate of the ship's position, to one decimal place.
Find the y-coordinate of the ship's position, to one decimal place.
Luke sailed for 116 kilometres on a bearing of 231 \degree.
If w is how many kilometres west he has sailed from his starting point, calculate w to one decimal place.
On an orienteering course, Valentina runs 1000 metres north from point A to point B, then turns east and runs to point C.
If the true bearing of C from A is 062 \degreeand the direct distance Valentina must run to get back to point A is d metres, calculate d to the nearest metre.
During a rescue search, a helicopter flew west from point X to point Y, then changed course and flew 10.7 \text{ km} north to point Z.
If point Z is on a bearing of 335 \degree \text{ T} from point X:
Find the size of \angle YXZ.
If the distance from point Y to point X is b \text{ km}, find b to one decimal place.
If the distance that the helicopter must fly between point Z and point X is d \text{ km}, calculate d to one decimal place.
Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38 \degree E from Ned.
If Ned and Bart are d metres apart, find d to one decimal place.
A yacht sailed in a direction so that its final position was 248 \text{ km} west and 225 \text{ km} south of its starting point.
If the bearing on which the yacht sailed is b \degree, find the value of b to one decimal place.
If the boat has sailed a total of d \text{ m}, find the value of d to one decimal place.
A rally car starts at point P and races 191 \text{ km} south to point Q. Here the car turns west and races for 83 \text{ km} to point R. At point R the car must turn to head directly back to point P.
Find a, to one decimal place.
Determine the compass bearing of P from R, to one decimal place.
Hence, determine the compass bearing of R from P, to one decimal place.
Carl goes for a walk and starts by travelling east. After walking for 137 \text{ m} , he then turns and walks north for 132 \text{ m} . What is the bearing of his staring position from where he is at the end of the walk? Give your answer correct to the nearest degree.
An aeroplane sets off on a bearing of 055 \degree. After some time, it needs to turn back and head to its original position. On what true bearing must it travel?
A boat sets off on a bearing of 121 \degree. After some time, it needs to turn back and head to its original position. On what true bearing must it travel?
During a navigation challenge, teams of scouts will either start at Camp A or Camp B and have to get to an unknown Camp C.
Camp B is at a bearing of 038 \degree \text{T} from Camp A, and Camp C must be at a bearing of 153 \degree \text{T} from Camp B due to the terrain.
The troop leader sets up Camp C so that it is an equal distance in a straight line from both camps A and B.
Complete the diagram by marking it with all known information.
Find the true bearing from Camp A to Camp C.
Tobias and Patricia are participating a hiking and orienteering activity with their school. At one point in the activity, they are trying to reach a checkpoint on a private farm fence that is 102.7\text{ m} from their position, at a bearing of 068\degree \text{ T}.
They can't travel to the checkpoint directly because they would be trespassing, so they decide to travel due east and then due north to get to the checkpoint.
How far east will Tobias and Patricia have to travel? Round your answer correct to two decimal places.
How far north will Tobias and Patricia have to travel? Round your answer correct to two decimal places.
In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 0 55 \degree. She then walked on a bearing of 145 \degree to point P, which is 916 \text{ m} due east of base.
State the size of \angle BSP.
Find the distance BS, to one decimal place.
Find the distance SP, to one decimal place.
If the photographer walks directly back to her base from point P, determine the total distance she would have travelled. Round your answer to one decimal place.
A fishing boat in search of large schools of fish sails from point A for 26 \text{ km} on a bearing of 205 \degree to point C. It then sails a further 24 \text{ km} on a bearing of 226 \degree to point E.
Find the sizes of the following:
If the boat is w \text{ km} west of its original starting point, find w to one decimal place.
If the boat is s \text{ km} south of its original starting point, find s to one decimal place.
Hence, if the boat is t \text{ km} from its starting point (as a straight line from A to E), find t to one decimal place.
If \theta \degree is the bearing of the boat from its starting point, find \theta to one decimal place.
