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.
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 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.
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.
