Worksheet: Angles of Elevation

In this worksheet, we will practice solving real-world problems using trigonometric functions in right triangles.

Q1:

A footballer kicks a ball into a goal post. The angle of elevation between the trajectory of the ball and the pitch is 3 8 . The ball hits the top of the goal post at a height of 2.44 m. Find the horizontal distance 𝑋 between the footballer and the goal giving the answer to two decimal places.

Q2:

Calculate the size 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.

  • A
  • B
  • C
  • D
  • E

Q3:

A truck travelled 1.5 km up a ramp which is inclined to the horizontal at an angle of 5 8 . Find the height at which the truck stopped giving the answer in metres to one decimal place.

Q4:

A ladder is leaning against a wall where the upper end is 4 m from the ground. The angle of inclination of the ladder to the ground is 4 0 . Find the horizontal distance between the base of the ladder and the wall giving the answer to two decimal places.

Q5:

The angle of elevation from a point 221 m away from the base of a minaret is 4 4 4 8 . Find the angle of elevation, to the nearest minute, if the point is now 202 m away from the base.

  • A 3 7 3 8
  • B 3 7 4 9
  • C 6 6 5 9
  • D 4 7 2 2
  • E 2 3 1

Q6:

A 175 cm tall man was standing on the ground 14 m away from a tree. The angle of elevation to the top of the tree was 3 4 4 8 . Find the height of the tree giving the answer to two decimal places.

Q7:

A lamp post 7.6 metres tall casts a 1.8 metres shadow. Find the angle of inclination of the sun giving the answer to the nearest minute.

  • A 1 3 1 9
  • B 1 3 4 2
  • C 8 5 4 9
  • D 7 6 4 1
  • E 7 6 1 8

Q8:

A man observed a stationary car from the top of a building. The car is on the same horizontal plane as the base of the building and 59 metres away. The angle of depression from the man to the car is 6 3 . Find the height of the building giving the answer to one decimal place.

Q9:

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 one mile is equal to 5 280 feet.

Q10:

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 6 0 . Assuming that the tree grows vertically, how far from the base of the tree is the point from which the angle was measured?

Q11:

A point on the ground is 32 metres away from the base of a house. The angle of elevation from the point to the roof of the house is 3 3 4 8 and the angle of elevation from the point to the top of the chimney is 3 8 3 6 . Find the height of the chimney giving the answer to two decimal places.

Q12:

A tower is 73 metres tall. A man observed the tower from a point and the angle of elevation was 3 6 . He then walked a horizontal distance of 𝑋 metres towards the tower and the angle of elevation was 5 9 3 0 . Find the value of 𝑋 giving the answer to one decimal place.

Q13:

The angle of elevation 64 metres away from the base of a minaret is 3 3 4 8 . Find the angle of elevation 6 metres away from the base of the minaret to the top of the minaret giving the answer to the nearest minute.

  • A 4 2 2 3
  • B 5 3 3 3
  • C 4 7 3 7
  • D 3 6 2 7

Q14:

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 6 0 , how far is the man from the base of the tree?

Q15:

The angle of elevation of the top of a New York building from a point on the ground one mile from the building is 9 . Find, in feet, the height of the building knowing that 1 mile = 5 2 8 0 feet. Give your answer to the nearest foot.

Q16:

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 4 0 and 2 3 respectively. Find the height of the flagpole accurate to two decimal places.

Q17:

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 1 5 . After walking for 0.5 miles on flat ground directly towards the stranded climber, the angle of elevation was 2 2 . What is the altitude of the climber in miles? Round your answer to one decimal place.

Q18:

The distance between two control towers, 𝐴 and 𝐵 at an airport is 2‎ ‎408 metres. The angles of elevation from the 𝐴 and 𝐵 to an aeroplane are 5 4 6 and 4 9 respectively. Find the altitude of the plane giving the answer to the nearest metre.

Q19:

Two students wanted to estimate the height of a building. They measured the angle of elevation of the top of the building from a point on the ground to be 3 9 . They moved 300 feet closer to the building and measured the angle of elevation of the top of the building to be 5 0 . They assumed the street to be level and used their results to calculate an estimate for the height of the building. What was their estimate to the nearest foot?

Q20:

A man and a woman standing 3 1 2 miles apart spot a hot air balloon at the same time. If the angle of elevation from the man to the balloon is 2 7 , and the angle of elevation from the woman to the balloon is 4 1 , find the altitude of the balloon to the nearest foot.

Q21:

A person measured the angle of elevation of a fixed hot air balloon as 𝜋 7 . He then walked 522 m in a horizontal direction towards the balloon and the angle of elevation was 𝜋 4 . Find the height of the hot air balloon to the nearest metre.

Q22:

A pole leans away from the sun at an angle of 7 to the vertical, as shown in the given figure. When the elevation of the sun is 5 5 , the pole casts a shadow 42 feet long on the level ground. How long is the pole? Round the answer to the nearest tenth.

Q23:

Two students wanted to estimate the height of a building. They measured the angle of elevation of the top of the building from a point on the ground to be 3 5 . They moved 250 feet closer to the building and measured the angle of elevation of the top of the building to be 5 3 . They assumed the street to be level and used their results to calculate an estimate for the height of the building. What was their estimate to the nearest foot?

Q24:

Two men are standing 685 metres apart on a horizontal field watching a fixed hot-air balloon. The angle of elevation of the first man to the top of the balloon is 4 5 and the angle of elevation of the second man to the top of the balloon is 2 7 . Find the vertical height of the balloon from the ground giving the answer to the nearest metre knowing that the projection of the ballon lies between the two men.

Q25:

A helicopter is moving vertically, above a point 𝐶 , with a uniform speed of 96 m/min. The angle of elevation from point 𝐴 on the ground is 2 4 and 3 minutes later becomes 8 . Find the distance between the points 𝐴 and 𝐶 giving the answer to the nearest meter.

  • A 647 m
  • B 955 m
  • C 133 m
  • D 945 m

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