A man standing at point C, is looking at the top of a tree at point A.
Identify the angle of elevation in the figure given.
A man standing at the top of the tower at point B, is looking at the ground at point C.
Identify the angle of depression in the figure given.
Find the value of x, the angle of elevation to point A from point C:
Round your answer to two decimal places.
Find the angle of depression, x, from point B to point C:
Round your answer to two decimal places.
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.
A helicopter is flying at an altitude of 198 \text{ m} from its landing pad, which is at an angle of depression of 44 \degree from the helicopter.
Determine the distance, d, between the helicopter and the landing pad. Round your answer to the nearest whole number.
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. Round your answer to the nearest metre.
Find the distance BC. Round your answer to the nearest metre.
Hence, find the distance covered by the jet in that one minute. Round your answer 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.
The angle of elevation to the top of a 22-metre high statue is 54 \degree from point A, due west of the statue. The point B is located 60 metres due south of point A.
Find the distance from point A to the base of the statue, correct to two decimal places.
Find the distance from point B to the base of the statue, correct to one decimal place.
Find the angle of elevation \theta, from point B to the top of the statue, correct to the nearest degree.
A room measures 5 \text{ m} in length and 4 \text{ m} in width. The angle of elevation from the bottom left corner to the top right corner of the room is 57 \degree.
Find d, the distance from one corner of the floor to the opposite corner of the floor. Leave your answer in surd form.
Find h, the height of the room. Round your answer to two decimal places.
Find the angle of elevation from the bottom corner of the 5 \text{ m} long wall to the opposite top corner of the wall, correct to two decimal places.
Find the angle of depression from the top corner of the 4 \text{ m} long wall to the opposite bottom corner of the wall, correct to two decimal places.
An airplane is currently flying 35 \degree south of east, 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 } 36 \degree \text{W} for 9 \text{ km} and 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 that represents its journey.
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.
Find the bearing of the clearing from the town, a \degree, to the nearest degree:
At a point during the flight, a plane is 42 \text{ km} south and 57 \text{ km} west of the airport it departs from:
Find the angle b to one decimal place.
Find the compass 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}.
Find the coordinates of the position of the ship, (x, y).
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.
A man drives 14 \text{ km} due east, and then 14 \text{ km} due north. Find 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.
Determine the compass bearing the hiker must have followed during the night.
Luke sailed for 116 kilometres on a bearing of 231 \degree.
Find how many kilometres west, w, he has sailed from his starting point.
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.
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.
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 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.
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.
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 bearing that the boat should travel on to return to the starting point.
