Lesson Worksheet: Angles of Elevation and Depression Mathematics

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

Q1:

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.

Q2:

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

  • A∠𝐴𝐢𝐡
  • B∠𝐴𝐡𝐢
  • C∠𝐡𝐴𝐢

Q3:

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.

Q4:

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.

Q5:

A body’s angle of depression from the top of a tower 77 meters tall is 2636β€²βˆ˜. 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 meter.

Q6:

The angle of elevation to the top of a skyscraper from a 30 m high house is 5842β€²βˆ˜. 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.

Q7:

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 4518β€²βˆ˜ and 3418β€²βˆ˜. Find the distance between the two points giving the answer to one decimal place.

Q8:

Two points on the ground lie collinearly on either side of a flagpole 5 meters tall. The angles of elevation from the two points to the top of the flagpole are 3618β€²βˆ˜ and 4230β€²βˆ˜. Find the distance between the two points in meters, giving the answer correct to one decimal place.

Q9:

Chloe wants to calculate the height of a tree in her garden. She stands at a perpendicular distance of 20 meters 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.

Q10:

From a point on the ground, the angle of elevation to the top of a tower that is 67 meters high is 36∘. Another point is 𝑋 meters horizontally closer to the base of the tower, where the angle of elevation is 57∘. Find the value of 𝑋, giving your answer to the nearest meter.

Q11:

A plane took off from a runway at an angle of elevation of 15∘. It continued to climb at the same constant angle. After 45 seconds, the plane reached a perpendicular height of 1,500 meters. What distance has the plane traveled in this time? Give your answer to two decimal places.

Q12:

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.

  • A310β€²10β€²β€²βˆ˜
  • B590β€²0β€²β€²βˆ˜
  • C4923β€²55β€²β€²βˆ˜
  • D4036β€²5β€²β€²βˆ˜

Q13:

Anthony 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. Anthony stands at a perpendicular distance of 85 ft from the base of the tree and measures the angle on his clinometer to be 54∘ as seen in the diagram. Given that Anthony’s eyeline is 6 ft from the ground, work out the height of the tree to the nearest foot.

Q14:

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 53∘. Find the distance between the point on the ground and the top of the mountain giving the answer to the nearest meter.

Q15:

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

Q16:

Daniel wants to find the height of a tower. 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. Daniel stands at a perpendicular distance of 100 ft from the base of the tower and measures the angle on his clinometer to be 59∘, as seen in the diagram.

Work out the angle of elevation.

Given that Daniel’s eyeline is 6 ft from the ground, work out the height of the tower to the nearest foot.

Q17:

Two boats lie on either side of a 170-meter-high rock, where the angles of depression from the top of the rock to the boats are 5448β€²βˆ˜ and 5918β€²βˆ˜ respectively. Determine the distance between the two boats to the nearest meter.

Q18:

The angle of elevation from the bottom of a 31-meter-tall tower to the top of a tree is 59∘. The angle of depression from the top of the tower to the top of the tree is 42∘. Find the height of the tree to the nearest meter.

Q19:

A man stands 50 meters away from the base of a tower. The angle of elevation from the top of the tower is 36∘. Find the height of the tower giving the answer to the nearest meter.

Q20:

In the given diagram, a 15 ft ladder is leaning against a wall with an angle of elevation of 70∘. How high up the wall would it reach? Give your answer to two decimal places.

Q21:

A 7.6-meter-tall streetlight casts a 1.8-meter shadow. Find the angle of inclination of the sun, giving the answer to the nearest minute.

  • A8549β€²βˆ˜
  • B1342β€²βˆ˜
  • C7618β€²βˆ˜
  • D7641β€²βˆ˜
  • E1319β€²βˆ˜

Q22:

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 40∘. Find the horizontal distance between the base of the ladder and the wall giving the answer to two decimal places.

Q23:

A man observes 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 meters away. The angle of depression from the man to the car is 63∘. Find the height of the building, giving the answer to one decimal place.

Q24:

A truck traveled 1.2 km up a ramp that is inclined to the horizontal at an angle of 4918∘. Find the height at which the truck stopped, giving the answer in meters to one decimal place.

Q25:

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 3448β€²βˆ˜. Find the height of the tree giving the answer to two decimal places.

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