Two flag posts of height 12 m and 17 m are erected 20 m apart.
Find the length, l, of the string needed to join the tops of the two posts. Round your answer to one decimal place.
Consider the diagram shown:
Find the length of AD, correct to two decimal places.
Find the length of BD, correct to two decimal places.
Hence, find the length of AB, correct to two decimal places.
For each of the following diagrams.:
Find y, correct to two decimal places.
Find w, correct to two decimal places.
Hence, find the value of x, correct to one decimal place.
In the following diagram, \angle CAE = 61 \degree, \angle CBE = 73 \degree and CE = 25.
Find the length of AE, correct to four decimal places.
Find the length of BE, correct to four decimal places.
Hence, find the length of AB, correct to two decimal places.
Find the length of BD, correct to one decimal place.
A jet takes off and leaves the runway at an angle of 34 \degree. It continues to fly in this direction for 7 \text{ min} at a speed of 630 \text{ km/h} before levelling out.
Find the distance in metres covered by the jet just before levelling out.
If the height of the jet just before levelling out is h \text{ m}, calculate h.
Round your answer to the nearest metre.
A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.
Find the height of the sand pile, h, to one decimal place.
Consider the given diagram:
Find the length of AC, to two decimal places.
Find the size of \angle ACB.
Find the size of \angle ACD.
Hence, find the length of CD, to one decimal place.
A suspension bridge is being built. The top of the concrete tower is 35.5 \text{ m} above the bridge and the connection point for the main cable is 65.9 \text{ m} from the tower.
Assume that the concrete tower and the bridge are perpendicular to each other.
Find the length of the cable to two decimal places.
Find the angle the cable makes with the road to two decimal places.
Identify the angle of depression from point B to point C in the given figure:
Find x, the angle of elevation to point A from point C. Round your answer to two decimal places.
At a certain time of the day a light post, 6\text{ m} tall, has a shadow of 8.5 \text{ m}. Find \theta, the angle of elevation from the end of the shadow to the sun at that time, to the nearest minute.
A helicopter is flying at an altitude of 198 \text{ m}. Its landing pad is at an angle of depression of 44 \degree.
Determine the distance, d, between the helicopter and the landing pad. Round your answer to the nearest whole number.
Sally measures the angle of elevation to the top of a tree from a point 20 \text{ m} away to be 43 \degree.
Find the height of the tree, h, to the nearest whole number.
The final approach of an aeroplane when landing requires the pilot to adjust the angle of depression to about 3 \degree as shown in the diagram below. If the plane is 12 \text{ m} above the runway and has d \text{ m} until touchdown, find d to the nearest metre.
A man stands at point A looking at the top of two poles. Pole 1 has a height 8 \text{ m} and an angle of elevation of 34 \degree from point A. Pole 2 has a height 25 \text{ m} and an angle of elevation of 57 \degree from point A.
Find x, the distance from A to B, to two decimal places.
Find y, the distance from A to C, to two decimal places.
Hence, find BC, the distance between the two poles in metres. Round your answer to one decimal place.
A fighter jet, flying at an altitude of 2000 \text{ m} is approaching an airport. The pilot measures the angle of depression to the airport to be 13 \degree. One minute later, the pilot measures the angle of depression again and finds it to be 16 \degree.
Find the distance AC, to the nearest metre.
Find the distance BC, to the nearest metre.
Hence, find the distance covered by the jet in that one minute, to the nearest metre.
Two towers stand on level ground. As shown in the diagram, the angles of elevation of the top of the taller tower from the top and bottom of the shorter tower are 7 \degree and 21 \degree respectively. The height of the taller tower is 72 \text{ m}.
Show that \theta=14 \degree.
Show that y = \dfrac{x \sin 14 \degree}{\sin 97 \degree}.
Show that x = \dfrac{72}{\sin 21 \degree}.
Hence, find the height of the shorter tower. Round your answer to the nearest metre.
Two towers AB and PQ stand on level ground. Tower AB is 14 \text{ m} taller than tower PQ. The angle of depression from point A to points P and Q are 32 \degree and 61 \degree respectively.
Use \triangle AKP to show that \\KP = 14 \tan 58 \degree.
Use \triangle ABQ to show that \\ AB = 14 \tan 58 \degree \tan 61 \degree.
Hence, find the height of the shorter tower. Round your answer to the nearest metre.
For the following diagram, use the sine rule to calculate the length of y in metres. Round your answer to one decimal place.
To find the distance ST across a river, a distance VT = 137\text{ m} is measured on one side of the river. It is found that \angle SVT = 33 \degree 38 ' and \angle VTS = 119\degree. If the distance ST is l\text{ m}, find l to one decimal place.
A golfer is at point G which is 65 \text{ m} from the hole, H. He plays a shot that lands at point B which is 12 \text{ m} from the hole. The direction of the shot was 6 \degree away from the line between G and H. The diagram shows the two possible positions of point B:
Find the two possible values of \angle GBH using these two possible positions of B. Round your answers to the nearest degree.
Hence, find the two possible distances the ball travelled, GB. Round your answers to one decimal place.
Consider point A in the following diagrams:
Find the true bearing of A from O.
Determine the compass bearing of point A from O.
Point P has a true bearing of 197 \degree \text{ T} from the origin O. Draw a diagram to represent this information.
The bearing of Point P from point O is \text{N }45 \degree \text{E}. Draw a diagram to represent this information.
Determine the true bearing of the following:
Northeast
Southeast
Southwest
Northwest
West-Northwest
South-Southeast
Consider the points P, M and S on the diagrams below where S denotes the south cardinal point. State the true bearing of P from M.
Determine the true bearing of point A from point B in the following bearings diagram:
If a person walks at a compass bearing of \text{SE}, and then turns around to go back in the direction they came, state the direction that they are heading now.
A man drives 14 \text{ km} due east, and then 14 \text{ km} due north. Find the compass bearing of his final position.
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.
During a group hike, a hiker walked 6 \text{ km} \text{ 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} \text{ NW} of the base camp.
Determine the compass bearing the hiker must have followed during the night.
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.
Consider the following diagram:
If the bearing of the clearing from the town is a \degree, find a to the nearest degree.
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.
An airplane is currently flying 35 \degree south of east towards point A, as shown in the diagram:
The control tower orders the plane to change course by turning 7 \degree to the left.
How many degrees south of east is the new course that the plane is ordered to fly?
A plane travels \text{N } 40 \degree \text{E} for 9 \text{ km} and 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 that represents its journey.
Consider the following diagram:
Find the true bearing of point C from point A.
Find the compass bearing of point C from point A.
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.
Luke sailed for 116 \text{ km} on a bearing of 231 \degree:
If w is the number of kilometres west he has sailed from his starting point, find w to one decimal place.
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.
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.
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 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.
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 the true bearing of A from C, to the nearest degree.
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.
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.
Find the size of \angle BAC.
Find the size of \angle ABC.
Determine how far Neil is from his starting point, A. Round your answer correct to two decimal places.
Point C has a bearing of 142 \degree from Point A. If Point B is 19 \text{ km} West of Point A, determine the distance, x, between Point B and Point C.
A ship sails 56 nautical miles on a bearing of 023 \degree. It then sails 81 nautical miles due east:
Find the size of angle \theta.
Calculate the distance x. Round your answer to the nearest nautical mile.
A ship sails 45\text{ km} from port A to port B on a bearing of 053 \degree, then sails 140\text{ km} from port B to port C on a bearing of 284 \degree.
Show \angle ABC = 51 \degree.
Find the distance of port A from port C to the nearest kilometre.
Find \angle ACB to the nearest degree.
Hence, find the bearing of port A from port C to the nearest degree.
A boat is sinking 2.2\text{ km} out to sea from a marina. Its bearing is 045 \degree from the marina and 320 \degree from a rescue boat. The rescue boat is due east of the marina.
Find the distance of the rescue boat from the sinking boat. Round your answer to two decimal places.
Find the time in minutes it takes the rescue boat to reach the sinking boat if it travels at 75\text{ km/h}. Round your answer to the nearest minute.
A motorbike and a car leave a service station at the same time. The motorbike travels on a bearing of 075 \degree and the car travels for 14.6\text{ km} on a bearing of 111 \degree until the bearing of the motorbike from the car is 310 \degree.
Calculate the travelled distance of the motorbike. Round your answer to one decimal place.
A submarine is being followed by two ships, A and B, with A \, \, 4.3\text{ km} due east of B. A is on a bearing of 164 \degree and B is on a bearing of 207 \degree from the submarine.
Find the following, rounding your answers to two decimal places:
The distance from the submarine to ship A.
The distance from the submarine to ship B.