# 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.

**Q1: **

Fill in the blank: The distance between two buildings is 40 m. The top of building has an angle of elevation of , measured from the top of building . If the height of building and the bases of the two buildings are on the same horizontal plane, then the height of to the nearest meter is m.

**Q2: **

From point on a riverbank, a man looked at a house located on the other side of the river at point and found the direction to be north of east. He walked 147 m east parallel to the river and arrived at point where point was north of east. Given the two riverbanks are parallel and points , , and are on the same horizontal level, find the width of the river giving the answer to the nearest metre.

**Q3: **

Two points on the ground lie collinearly on one side of a flagpole which is 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.

**Q4: **

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 and 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.

**Q5: **

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 . Victoria stands directly behind Anthony, she measures the angle of elevation, from the ground, to be . They both calculate the same height for the statue. How far behind Anthony must Victoria be standing? Give your solution to two decimal places.

**Q6: **

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

**Q7: **

A boat was sailing in a straight line toward a rock with a uniform velocity of 96 m/min. At one point, the angle of elevation to the top of a rock was , and 3 minutes later it became . Find the height of the rock giving the answer to the nearest meter.

**Q8: **

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

**Q9: **

A tower is 33 meters tall. The angle of depression from the top of a hill to the top of the tower is . The angle of depression from the top of the hill to the bottom of the tower is . 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.

**Q10: **

The angle of elevation of the top of a hill from its base is . A man climbs the hill from that point at an angle of to the horizontal for a distance of 340 meters. His path then continues to the top at an angle of to the horizontal. Find the height of the hill to the nearest meter.