Worksheet: Angles of Elevation and Depression

In this worksheet, we will practice solving real-world problems that involve angles of elevation and depression.

Q1:

A building is 8 meters tall. The angle of elevation from the top of the building to the top of a tree is 44 and the angle of depression from the top of the building to the base of the tree is 58. Find the distance between the base of the building and the base of the tree giving the answer to two decimal places.

Q2:

The height of a lighthouse is 60 meters. The angles of elevation between two boats in the sea and the top of the lighthouse are 29 and 39, respectively. Given that the two boats and the base of the lighthouse are colinear and that the boats are both on the same side of the lighthouse, find the distance between the two boats giving the answer to the nearest meter.

Q3:

A ladder is leaning against a wall where the upper end is 4.5 m high from the ground. The angle of inclination of the ladder to the ground is 41. Find the length of the ladder giving the answer to two decimal places.

Q4:

In the given diagram of a ladder leaning against a wall, which of the following angles represents the ladder’s angle of elevation?

  • A 𝐴 𝐶 𝐵
  • B 𝐴 𝐵 𝐶
  • C 𝐵 𝐴 𝐶

Q5:

A man who is 1.7 meters tall is standing in front of a 4.3-meter-high streetlight. When the streetlight is turned on, the man’s shadow is 2.2 meters long. Find the distance between the man and the base of the streetlight, giving the answer to two decimal places.

Q6:

Anthony and Victoria want to find the height of a statue. Anthony stands 5 meters from the base of the statue and measures the angle of elevation, from the ground, to be 65. Victoria stands directly behind Anthony, she measures the angle of elevation, from the ground, to be 30. They both calculate the same height for the statue. How far behind Anthony must Victoria be standing? Give your solution to two decimal places.

Q7:

Amelia and Noah stand at the base of a building on a flat, level ground. They both look up at a television antenna fixed at the top of the building. Amelia stands 30 feet from a point at the base of the building and Noah stands 25 feet away from that point. The angle of elevation from the floor where Amelia stands to the TV antenna is 62. Answer the following, giving your solutions to two decimal places.

Work out the height of the building.

Work out the angle of elevation from the point where Noah stands to the TV antenna.

Q8:

A flag is hung 22 meters up a flagpole. As the flag is raised, the angle of elevation from a point 21 meters away from the base of the flagpole to the flag is 74. Find the increase in height of the flag giving the answer to two decimal places.

Q9:

If a 20-feet building has a 55-foot shadow, what is the angle of elevation of the top of the building from the tip of the shadow?

Q10:

A ship was approaching a 49-metre-high lighthouse. At point 𝐴, the angle of elevation to the top of the lighthouse was 0.44 rad, and, 12 minutes later, at point 𝐵, it was 0.3 rad. Find the uniform speed of the ship from 𝐴 to 𝐵 giving the answer in metres per minute to one decimal place.

Q11:

A body’s angle of depression from the top of a tower 77 metres tall is 2636. Find the distance between the body and the base of the tower given both the body and the tower’s base are located on the same horizontal level. Give the answer to the nearest metre.

Q12:

The angle of elevation to the top of a skyscraper from a 30 m high house is 5842. The base of the house is 45 meters away from the base of the skyscraper. Find the height of the skyscraper giving the answer to two decimal places.

Q13:

Two points on the ground lie collinearly on either side of a flagpole 29 meters tall. The angles of elevation from the two points to the top of the flagpole are 4518 and 3418. Find the distance between the two points giving the answer to one decimal place.

Q14:

A man was standing on the ground 28 m away from the base of a tower that had a flagpole on its top. He measured the angles of elevation of the top and the base of the flagpole and found them to be 4330 and 2212 respectively. Find the height of the flagpole, giving the answer to the nearest metre, neglecting the height of the man.

Q15:

A point on the ground lies 129 metres away from the base of a tower. The angle of elevation from the point to the top of the tower is 36. Find the additional height of the tower needed for the angle of elevation to be 57 from the point. Give the answer to the nearest metre.

Q16:

Two points on the ground lie collinearly on either side of a flagpole 5 metres tall. The angles of elevation from the two points to the top of the flagpole are 3618 and 4230. Find the distance between the two points in metres, giving the answer correct to one decimal place.

Q17:

Lily wants to calculate the height of a tree in her garden. She stands at a perpendicular distance of 20 metres from the base of the tree. Using a clinometer, she measures the angle of elevation from the ground to the top of the tree as 52. Work out the height of the tree. Give your solution to two decimal places.

Q18:

The height of a giant redwood tree is known to be 370 feet. The angle of elevation from a point on horizontal ground to the top of the tree is 60. Assuming that the tree grows vertically, how far from the base of the tree is the point from which the angle was measured?

Q19:

A man was standing 25 m away from the base of a tower with a flagpole at the top. He measured the angles of elevation of the top and the base of the flagpole to be 40 and 23 respectively. Find the height of the flagpole accurate to two decimal places.

Q20:

Assuming that a 370-foot tall giant redwood grows vertically, if a man walks a certain distance from the tree and measures the angle of elevation to the top of the tree to be 60, how far is the man from the base of the tree?

Q21:

The angle of elevation of the top of a building in New York from a point on the ground 2 miles from the base of the building is 2. Find the height of the building in feet. Note that 1 mile is equal to 5,280 feet.

Q22:

What percentage grade should a road have if the angle of elevation of the road is 4 degrees? The percentage grade is defined as the change in the altitude of the road over a 100-foot horizontal distance. For example, a 5% grade means that the road rises 5 feet for every 100 feet of horizontal distance.

  • A 7 %
  • B 5 %
  • C 9 9 %
  • D 6 %
  • E 2 0 %

Q23:

A climber is stranded on a cliff face. A rescue team leaves immediately from their base, which is at an altitude of 1 mile, and heads directly towards the climber. When the team left the base the angle of elevation from them to the climber was 15. After walking for 0.5 miles on flat ground directly towards the stranded climber, the angle of elevation was 22. What is the altitude of the climber in miles? Round your answer to one decimal place.

Q24:

The distance between two control towers is 1,637 meters. An airplane is departing the airport and momentarily it is directly above the straight line between 𝐴 and 𝐵. At this moment, the angles of elevation from the bases of towers 𝐴 and 𝐵 are 3524 and 3348, respectively. Find the altitude of the plane, giving the answer to the nearest meter.

Q25:

Calculate the measure of the angle of elevation of the top of a 10 m high building from a point on the ground 8 m from its base, giving the answer to two decimal places.

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