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Worksheet: Angles of Elevation and Depression

Q1:

In the figure below 𝐢 𝐷 represents a hill and 𝐴 𝐡 represents a tower with a height of 27 metres. The angles of depression from 𝐢 to 𝐴 and 𝐡 are 2 1 ∘ and 4 2 4 2 β€² ∘ respectively. Find the height of the hill giving the answer to the nearest metre.

Q2:

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 4 1 ∘ . Find the length of the ladder giving the answer to two decimal places.

Q3:

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 𝐢 𝐡
  • B ∠ 𝐴 𝐡 𝐢
  • C ∠ 𝐡 𝐴 𝐢

Q4:

A tower is 33 meters tall. The angle of depression from the top of a hill to the top of the tower is 3 1 ∘ . The angle of depression from the top of the hill to the bottom of the tower is 5 2 ∘ . Find the height of the hill given the bases of the hill and the tower lie on the same horizontal level. Give the answer to the nearest meter.

  • A 101 m
  • B 49 m
  • C 41 m
  • D 62 m

Q5:

A minaret is 7 5 meters tall. From the top of a tower, the angles of depression of the top and the base of the minaret are 3 2 ∘ and 5 2 ∘ , respectively. Find the distance between the base of the minaret and the tower, given that the bases lie on the same horizontal plane. Give the answer to the nearest meter.

  • A 59 m
  • B 186 m
  • C 147 m
  • D 114 m

Q6:

A point is located 18 meters away from the base of a 21-meter high house. Find the angle of elevation from the point to the top of the house.

  • A 3 1 0 β€² 1 0 β€² β€² ∘
  • B 5 9 0 β€² 0 β€² β€² ∘
  • C 4 0 3 6 β€² 5 β€² β€² ∘
  • D 4 9 2 3 β€² 5 5 β€² β€² ∘

Q7:

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

  • A 1.33 meters
  • B 5.56 meters
  • C 1.26 meters
  • D 3.36 meters
  • E 3.86 meters

Q8:

Two gas stations, 𝐴 and 𝐡 , are 4.3 km apart on a straight and level highway. From a plane flying above the highway, the angles of depression of 𝐴 and 𝐡 are 3 2 ∘ and 5 6 ∘ respectively. Find the distance of the plane from station 𝐴 . Give your answer to one decimal place.

Q9:

Noah wants to find the height of an oak tree in his garden. He decides he needs to make a clinometer in order to measure the angle of elevation. He uses a straw, a protractor, some string, and a bit of Blu-Tack as a weight. Noah stands at a perpendicular distance of 85 ft from the base of the tree and measures the angle on his clinometer to be 5 4 ∘ as seen in the diagram. Given that Noah’s eyeline is 6 ft from the ground, work out the height of the tree to the nearest foot.

Q10:

A mountain is 8.78 km tall from the ground. The angle of elevation of the top of the mountain from a point on the ground is 5 3 ∘ . Find the distance between the point on the ground and the top of the mountain giving the answer to the nearest metre.

Q11:

A passenger on a ship gazes towards the mountainous shore and notices that, from where he stands, the summit of one mountain lies directly behind the summit of another; both summits are 4 3 ∘ west of north from him. 4 hours later, he looks for the two mountains again, and finds that they no longer line up; one is 1 8 ∘ south of west from him and the other is 2 7 ∘ north of west. Given that the ship he is on was travelling northeast at a speed of 34 km/h, find the distance between the two mountains.

Q12:

The vertical height of a rock is 88 meters. The angles of depression from the top of the rock to the top and the base of a tower are 2 4 ∘ and 3 7 ∘ respectively. Find the height of the tower given the base of the rock and tower lie on the same horizontal level. Give the answer to the nearest meter.

  • A 117 m
  • B 52 m
  • C 124 m
  • D 36 m

Q13:

A boat is 277 metres away from the base of a cliff which is 157 metres high. Find the size of the angle of depression from the top of the cliff to the boat. Give the answer in radians to two decimal places.

Q14:

An angle of depression is the acute angle formed between a horizontal line and an observer’s line of sight to an object below the horizontal. Two gas stations, 𝐴 and 𝐡 , are 6.6 km apart on a straight and level highway. From a plane flying above the highway, the angles of depression of the gas stations are 3 7 ∘ and 4 4 ∘ respectively. Find the distance of the plane from station 𝐴 . Give your answer to one decimal place.