Identify the angle of elevation from point C to point A in the given figure:
Identify the angle of depression from point B to point C in the given figure:
Consider the diagram where angle x is the angle of elevation to point A from point C.
Write a trigonometric equation to solve for angle x.
Solve the equation from part (a) to find the size of angle x. Round your answer to two decimal places.
Given that angle x and y are complementary, find the size of angle y.
Consider point A in the following diagrams:
Find the true bearing of A from O.
Determine the compass bearing of point A from O.
Determine the true bearing of the following:
Northeast
Southwest
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:
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.
Sally measures the angle of elevation to the top of a tree from a point 20 \text{ m} away to be 43 \degree.
Write a trigonometric equation to solve for the height, h, of the tree.
Find the height of the tree, h, to the nearest whole number.
During a particular time of the day, a tree casts a shadow of length 24\text{ m}. The height of the tree is estimated to be 7\text{ m}.
Find the angle \theta, formed by the length of the shadow and the arm extending from the edge of the shadow to the height of the tree. Round your answer to two decimal places.
Find the height of the tree, h, to two decimal places:
The person in the picture sights a pigeon above him. Find \theta to two decimal places.
A boy flying his kite releases the entire length of his string which measures 27\text{ m}, so that the kite is 18\text{ m} above him.
If the angle the string makes with the horizontal ground is \theta, find \theta to two decimal places.
A slide casts a shadow 5.66 \text{ m} along the ground. The distance between the tip of the shadow and the top of the slide is 7.84\text{ m}.
Find \theta to two decimal places.
If d is the distance between the base of the wall and the base of the ladder, find the value of d to two decimal places.
A ladder measuring 1.65 \text{ m} in length is leaning against a wall. If the angle the ladder makes with the wall is y \degree, find y to two decimal places.
The final approach of an aeroplane when landing requires an angle of descent of about 4 \degree.
If the plane is directly above a point 51 \text{ m} from the start of the runway, find d, the height of the plane above the ground to the nearest metre.
A 13.7 \text{ m} long string of lights joins the top of a tree to a point on the ground. If the tree is 3.7 \text{ m} tall, find \theta, the angle the string of lights would make with the tree, rounded to two decimal places.
Jack is standing at the tip of a tree's shadow and knows that the angle from the ground to the top of the tree is 34 \degree. If Jack is standing 29 \text{ m} away from the base of the tree, find the height of the tree to two decimal places.
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.
The final approach of an aeroplane when landing requires the pilot to adjust the angle of descent 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 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 covered by the jet in that one minute, to the nearest metre.
Amelia measures the angle of elevation to the top of a tree from a point, 29 \text{ m} away from the base, to be 31 \degree. Find the height of the tree, h, to the nearest metre.
The angle of elevation from an observer to the top of a tree is 18 \degree. If the distance between the tree and the observer is d \text{ m} and the tree is known to be 3.53 \text{ m} high, find the value of d to two decimal places.
From the top of a rocky ledge 188 \text{ m} high, the angle of depression to a boat is 13 \degree. If the boat is d \text{ m} from the foot of the cliff, find the value of d correct to two decimal places.
At a certain time of the day a light post, 6 \text{ m} tall, has a shadow of 5.8 \text{ m}. If the angle of elevation of the sun at that time is \theta \degree, find \theta to two decimal places.
Lisa is on a ship and observes a lighthouse on a cliff in the distance. The base of the cliff is 906 \text{ m} away from the ship, and the angle of elevation of the top of the lighthouse from Lisa is 16 \degree.
If the top of the lighthouse is x \text{ m} above sea level, find the value of x correct to two decimal places.
If the lighthouse is 21 \text{ m} tall, how tall is the cliff? Round your answer to two decimal places.
Buzz is standing 49 \text{ m} from a building and measures the angle of elevation of the top of the building to be 23 \degree.
If the difference in height between the top of the building and Buzz's eye is h \text{ m} , find the value of h correct to two decimal places.
If Buzz's eye is 135\text{ cm} from the ground, what is the height of the building? Round your answer to one decimal place.
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 the distance from A to B, to two decimal places.
Find 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 ship dropped anchor off the coast of a resort. The anchor fell 65 \text{ m} to the sea bed. During the next 5 hours, the ship drifted 120 \text{ m}. Calculate the angle of depression, x, between the anchor line and the surface of the water, rounded to the nearest degree.
A ramp of length 311\text{ cm} needs to ascend at an angle between 10 \degree and 20 \degree for it to be safe to use.
If the height of the ramp is 152\text{ cm}, and the angle the ramp makes with the ground is x, find x to two decimal places.
If the height of the ramp is 25\text{ cm} , and the angle the ramp makes with the ground is y, find y to two decimal places.
If the height of the ramp is 100\text{ cm}, and the angle the ramp makes with the ground is z, find z to two decimal places.
Hence, at which height is the ramp safe?
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.
The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10\,369 \text{ m} above the ground and is still 23\,444 \text{ m} from the runway.
If \theta \degree is the angle at which the plane should approach, find \theta to one decimal place.
During rare parts of Mercury and Venus' orbit, the angle from the Sun to Mercury to Venus is a right angle, as shown in the diagram:
The distance from Mercury to the Sun is 60\,000\,000\text{ km}. The distance from Venus to the Sun is 115\,000\,000\text{ km}.
What is the angle \theta, from Venus to the Sun to Mercury? Round your answer to the nearest minute.
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.
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.
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.
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.
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.
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 from A to C , 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 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.
