10 Questions
What is the line drawn from the eye of an observer to the point in the object viewed called?
Line of sight
In trigonometry, what is the angle formed by the line of sight with the horizontal called when the point being viewed is above the horizontal level?
Angle of elevation
In a situation where the line of sight is below the horizontal level, what is the angle formed by the line of sight with the horizontal called?
Angle of depression
What does the angle BAC represent in Fig. 9.1?
Angle of elevation
When a person raises their head to look at an object, which angle is formed between the line of sight and the horizontal?
Angle of inclination
What is the primary application of trigonometry in Fig. 9.1?
Height of tower calculation
In a scenario where a girl looks down at an object placed below her eye level, what type of angle is formed with the horizontal?
Angle of depression
What does trigonometry help calculate when applied to heights and distances?
$Distance between two points$
Which angle represents looking upwards at an object in trigonometry terminology?
$90^{\circ}$ angle
When would you typically encounter an angle of inclination?
When measuring vertical distances.
Study Notes
Angles of Elevation and Depression
- The angle of elevation of a point is the angle formed by the line of sight with the horizontal when the point is above the horizontal level.
- The angle of depression of a point is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.
Measuring Heights and Distances
- To find the height of an object (minar) without measuring it, you need to know: • The distance from the foot of the object (DE) • The angle of elevation ( BAC) of the top of the object • The height of the observer (AE)
- The height of the object (CD) can be calculated using trigonometric ratios: CD = CB + AE, where CB can be found using tan A or cot A.
Problem-Solving Applications
- Angle of depression can be used to find the distance between two ships observed from the top of a lighthouse.
- Angle of elevation can be used to find the distance travelled by a balloon moving with the wind.
- Angle of depression can be used to find the time taken by a car to reach the foot of a tower from a given point.
Summary
- The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
- The angle of elevation is the angle formed by the line of sight with the horizontal when the point is above the horizontal level.
- The angle of depression is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.
This quiz discusses the concepts of angles of elevation and angles of depression, including how to identify them in different scenarios. It also includes practical examples involving finding heights of objects using trigonometry. Test your understanding of these concepts with this quiz!
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