# 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 . 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 ladderβs angle of elevation?

- A
- B
- C

**Q5: **

A bodyβs angle of depression from the top of a tower 77 meters tall is . Find the distance between the body and the base of the tower given both the body and the towerβs 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 . 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 and . 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 and . 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 . 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 . Another point is meters horizontally closer to the base of the tower, where the angle of elevation is . Find the value of , giving your answer to the nearest meter.

**Q11: **

A plane took off from a runway at an angle of elevation of . 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.

- A
- B
- C
- D

**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 as seen in the diagram. Given that Anthonyβs eyeline is 6 ft from the ground, work out the height of the tree to the nearest foot.

**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 , as seen in the diagram.

Work out the angle of elevation.

Given that Danielβs 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 and 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 . The angle of depression from the top of the tower to the top of the tree is . 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 . 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 . 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.

- A
- B
- C
- D
- E

**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 . Find the height of the building, giving the answer 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 . Find the height of the tree giving the answer to two decimal places.