Trigo: Angle Of Elevation & Depression
In this video lesson, we are going to cover the concepts of angle of elevation & depression.
Angles of elevation and depression in trigonometry are used to describe the angle formed between a horizontal line and a line of sight. The angle of elevation is the angle measured upwards from the horizontal when looking at an object above eye level, while the angle of depression is measured downwards when looking at an object below eye level.
These angles are often used together with trigonometric ratios such as sine, cosine, and tangent to find unknown heights or distances in real-life situations, such as determining the height of a building or the distance between two points.
Related Lessons:
How To Measure Angle Of Elevation & Depression
When measuring angles of elevation and depression, students should take note of a few important points:
- These angles are always measured from the horizontal line (the horizon), not the vertical—this is a common mistake
- If the line of sight is directed below the horizontal, the angle formed is called the angle of depression.
- If the line of sight is directed above the horizontal, it is called the angle of elevation.
Practical Application: Measure Building Height
In this video, we will explore a practical application of how to measure the height of a building using mathematical techniques. This is especially useful for students who need to carry out school projects involving measuring the height of objects, such as a flagpole or a building, within their school environment.
Example 1
- the angle of elevation of the top of the lighthouse H from B
- the height of the lighthouse CH
Example 2
A hot air balloon was tied with a 300m rope to the bottom of a tree. At first, the angle between the rope and the ground was 70° and finally decreased to 35°. Find the vertical distance that the hot air balloon descended.