State the compass direction that is opposite to:
\text{N}
\text{W}
\text{SE}
\text{SW}
\text{NNE}
\text{WNW}
For each of the following, state the bearing that describes the compass direction:
Start at North and rotate 30\degree towards West
Start at South and rotate 58\degree towards East
The bearing of Point P from point O is \text{N }45 \degree \text{E}. Draw a diagram to represent this information.
If a person walks at a compass bearing of \text{SE}, and then turns around to go back in the direction they came. What direction are they heading in now?
Draw the direction \text{NNW} on a compass rose.
Consider the points P, A and N on the diagram where N denotes the north cardinal point.
State the true bearing of P from A.
Consider the points , P, M and S on the diagrams below, where S denotes the south cardinal point. Using the diagram, find the true bearing of P from M.
Determine the true bearing of the following:
North
East
South
West
Northeast
Southeast
Southwest
Northwest
West-Northwest
South-Southeast
Write the following true bearings as compass directions:
270\degree\text{ T}
000\degree\text{ T}
45\degree\text{ T}
225\degree\text{ T}
315\degree\text{ T}
022.5\degree\text{ T}
198\degree\text{ T}
337\degree\text{ T}
Point P has a true bearing of 197 \degree \text{ T} from the origin O. Draw a diagram to represent this information.
Determine the true bearing of point B from point A in the following bearings diagram:
Determine the true bearing of point A from point B in the following bearings diagram:
Consider point A in the following diagrams:
Find the true bearing of A from O.
Determine the compass bearing of point A from O.
In the figure below, point B is due East of point A:
Find the true bearing of point A from point C.
Find the compass bearing of point A from point C.
Consider the following diagram:
Find the true bearing of point B from point C.
Find the compass bearing of point B from point C.
Consider the following diagram:
Find the true bearing of point C from point A.
Find the compass bearing of point C from point A.
Consider the following diagram:
Find the true bearing of point C from point B.
Find the compass bearing of point C from point B.
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 boat sets off on a bearing of 058 \degree \text{ T}. After some time, it needs to turn back and head to its original position. Find the true bearing it must travel.
A yacht sets off on a bearing of 128 \degree \text{ T}. After some time, it needs to turn back and head to its original position. Find the true bearing it must travel.
Consider the following diagram:
If the bearing of the clearing from the town is a \degree, find a to the nearest degree.
A boat travelled 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.
Write the bearing of the boat from its starting point as a true bearing.
Shortly after take-off, 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.
State the true bearing of the plane from the airport.
The position of a ship S is given to be 20 \text{ km} from P, on a true bearing of 0 49 \degree \text{ T}. The position of the ship can also be given by its \left(x, y\right) coordinates.
Find the ship's x-coordinate to one decimal place.
Find the ship's y-coordinate to one decimal place.
Luke sailed for 116 \text{ km} on a bearing of 231 \degree.
If w is how many kilometres west he has sailed from his starting point, find w to one decimal place.
On an orienteering course, Valentina runs 550 \text{ m} north from point A to point B, then turns east and runs to point C.
If the true bearing of C from A is 041 \degree \text{ T}, find the distance, d, to the nearest metre.
Three television presenters are practising their navigation skills before heading off on an expedition to a remote location.
Belinda at point B is positioned 17.6 \text{ m} south of Amelia at point A. Carl at point C is due east of Belinda and on a bearing of \text{S } 38 \degree \text{E} from Amelia.
If Amelia and Carl are d \text{ m} apart, find d to one decimal place.
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.
A pilot flies 12 \text{ km} due east, and then 12 \text{ km} due north. Determine the compass bearing of his final position, from his starting position.
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 true 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 angle 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.
Christa and James set off for a walk. They leave Point A 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 true the bearing of A from C, to the nearest degree.
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.
Grenada \left(G\right), Tangiers \left(T\right) and Roma \left(R\right) are three towns. Grenada is on a bearing of 31 \degreefrom Tangiers and 312 \degreefrom Roma. Tangiers is due west of Roma. The distance from Grenada to Roma is 55 \text{ km}.
Find the distance from Grenada to Tangiers, x, to the nearest kilometre.
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 true bearing of the boat from its starting point, find \theta to one decimal place.
A boat travels \text{S } 14 \degree \text{E} for 12 \text{ km} and then changes direction to \text{S } 49 \degree \text{E} for another 16 \text{ km}.
Find x, the distance of the boat from its starting point to two decimal places.
Find b to the nearest degree.
Hence, find the compass bearing that the boat should travel on to return to the starting point.
A pod of dolphins following warm ocean currents were tracked travelling 7.7 \text{ km} from Ryla to Luna on a bearing of 219 \degree, and then 9.2 \text{ km} to Elara which is 13.6 \text{ km} due south of Ryla.
Find \theta, the angle at which they changed direction when they got to Luna. Round your answer to one decimal place.
Hence, find the true bearing of Elara from Luna.
A drone travels due east for 2.2 \text{ km} and then travels on a bearing of \text{S } 32 \degree \text{E} for 5.9 \text{ km}.
Determine the compass bearing needed to return to the staring point, to the nearest degree.
Neil travelled on a bearing of 26 \degree from Point A to Point B. He then travelled on a bearing of 121 \degree for 18 \text{ km} towards Point C, which is due East from point A.
Determine how far Neil is from his starting point, A. Round your answer correct to two decimal places.
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 true bearing that the passenger plane must fly from point A to reach the smaller plane at point C.
Point C is 23 \text{ km} away from Point A on a bearing of 142 \degree. If Point B is 19 \text{ km} West of Point A, determine the distance, x, between Point B and Point C.
Dave leaves town along a road on a bearing of 169 \degree and travels 26 \text{ km}. Maria leaves the same town on another road with a bearing of 289 \degree and travels 9 \text{ km}.
Find the direct distance between Dave and Maria. Round your answer to the nearest kilometre.