Introduction: Trigonometry, is often used in the measurement of heights and distances of objects which can not be measured by physical measuring devices. For example, trigonometry was used to find the distance of stars from the Earth. Even today, in spite of more accurate methods being available, trigonometry is often used for making quick and simple calculations regarding heights and distances of far-off objects. In this chapter, we shall apply the trigonometric ratios to solve the problems regarding heights and distances of various objects without measuring them.
To apply trigonometric ratios to find the distance or the height of the object certain terms should be clear to us. Let us consider the case of an object as shown in the figure below
Horizontal Level: A horizontal level is a line which is parallel to the ground . In the figure line BC represents the horizontal level.
Line of Sight: When the human eye looks at some object then the line made by the vision to the object is called the Line of Sight.In the figure the eye is at point C (eye) and the object is placed at point A. Then the straight line AC between the eye and the object is called the line of sight.
Illustration: Identify the line of sight and horizontal level for the object at point C in the figure when the eye of the observer is at point B
Solution: When the object is at Point C and the eye of the observer is at B then
Line of sight is represented by BC
Horizontal Level is represented by BD
Identify the line of sight for the object at point A in the figure when the eye of the observer is at point B | |||
Right Option : A | |||
View Explanation |
Identify the Horizontal level for the object at point A in the figure when the eye of the observer is at point B | |||
Right Option : C | |||
View Explanation |
Identify the Horizontal level and line of sight respectively for the object at point A in the figure when the eye of the observer is at point B | |||
Right Option : C | |||
View Explanation |
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