A man standing at point C, is looking at the top of a tree at point A. Identify the angle of elevation in the following figure:
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 following figure:
Find the angle of depression from point B to point C in the diagram shown. Round your answer to two decimal places.
Find x, the angle of elevation to point A from point C. Round your answer to two decimal places.
The side AC has a length of 57 \text{ m} and the angle of depression from C to B is 40 \degree:
Find the length of AB, correct to two decimal places.
The side AB has a length of 11 \text{ m} and the angle of elevation from A to C is 28 \degree:
Find the length of AC, correct 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:
Find the distance, d, between the helicopter and the landing pad. Round your answer to the nearest whole number.
Maria and her friends are at a rock concert, enjoying one of their favourite bands. The lead singer is 68 \text{ m} across and 20 \text{ m} down from where Maria is in the stadium:
Calculate the angle of depression, x, from Maria to the lead singer. Round your answer to the nearest degree.
Isabelle and Harry are visiting a museum, on top of which there is a viewing platform. Isabelle goes up to the viewing platform, while Harry goes outside to get ice cream.
If Isabelle is now 22 \text{ m} vertically above Harry, and the angle of elevation from Harry to Isabelle is 34 \degree 42 ', then find the direct distance between them, x \text{ m}, correct to two decimal places.
Lachlan occasionally has staring contests with his cat.
If Lachlan is 152 \text{ cm} tall and his cat is sitting 311 \text{ cm} away from him, find the angle of elevation, \theta, from the cat to Lachlan, correct to the nearest degree.
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.
At a certain time of the day, a light post, 7 \text{ m} tall, has a shadow of 7.7 \text{ m}. If the angle of elevation of the sun at that time is \theta, find \theta correct to the nearest minute.
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.
Eileen decides to try out parasailing, which involves gliding through the air with a parachute, while being pulled along by a motor boat.
The string attaching Eileen to the motor boat is 94 \text{ m} long, and at one point while parasailing, the angle of depression from Eileen to the boat is 40 \degree 13 '.
Find Eileen's vertical height from the boat, h\text{ m}, correct to two decimal places.
Describe what would happen to the angle of depression if Eileen's height from the water increased.
A football player 1.6 \text{ m} tall is attempting a free kick through goal posts and over a bar that is 4.8 \text{ m} above ground and 43.5 \text{ m} away from where he is standing.
Find the angle that the player needs to look up to focus on the bar. Round your answer to the nearest minute.
Amelia is watching the Sydney to Hobart yacht race from the top of a cliff, at a position that is 109 \text{ m} above sea level. At one point of the race, she spots her friend's yacht at a distance of 131 \text{ m} directly away from where she is standing.
Find the angle of depression from Amelia to the yacht, correct to the nearest minute.
Neil is practicing for a professional basketball game and tries to throw the ball into the hoop when he is 457.2 \text{ cm} away from the backboard. Neil is 201.2 \text{ cm} tall, and the top of backboard is at a height of 425.6 \text{ cm}.
Find x, the angle of elevation from Neil to the top of the backboard. Round your answer to the nearest minute.
Find y, the angle of depression from Neil to the point on the ground directly below the backboard. Round your answer to the nearest minute.
From the cockpit of an aeroplane flying at an altitude of 3000 \text{ m}, the angle of depression to the airport is 57 \degree. The aeroplane continues to fly in the same straight line, and after a few minutes, the angle of depression to the airport becomes 67 \degree.
The horizontal distance between the cockpit at the first sighting and the point directly above the airport is x \text{ m}.
Find the value of x. Round your answer to one decimal place.
The horizontal distance between the cockpit at the second sighting and the point directly above the airport is y \text{ m}.
Find the value of y. Round your answer to one decimal place.
Find the distance between the two sightings. 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.
A ship drops an anchor of length 81 \text{ m} to the bottom of the sea floor when the back of the ship is 244 \text{ m} away from a cliff-face. From the ship, there is an angle of elevation of 38 \degree to the top of the cliff, and an angle of depression of 59 \degree to the anchor.
Find the total height of the cliff, giving your answer correct 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.
From the top of a cliff, 47 \text{ m} above sea level, two boats are observed to be in the same direction. Their angles of depression from the top of the cliff are 12 \degree and 23 \degree.
Find the distance between the base of the cliff and the boat furthest away, correct to two decimal places.
Find the distance between the base of the cliff and the closest boat, correct to two decimal places.
Hence, find the distance between the two boats in metres, correct to one decimal place.