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| Heights and Distances |
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| One of the main use of trigonometry is to find the distances between points, or the heights of objects, without actually measuring these distances or these heights. |
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| Angle of elevation |
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| Let O = Position of the observer |
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| P = Position of the object |
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| OH = Horizontal line through O (line of reference) |
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| Angle of depression |
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| Let O = Position of the observer |
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| P = Position of the object |
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| OH = Horizontal line through O (line of reference) |
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| Example: |
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| A person standing on the bank of a river, observes that the angle subtended by a tree on the bank is 60o. When he retreats 20m from the bank, he finds the angle to be 30o. Find the height of the tree and the breadth of the river. |
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| Suggested answer: |
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| In the adjoining figure, |
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| AB = width of river = x |
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| BC = height of tree = h |
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| OA = 20m |
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| O is the position of the person after retreating 20m from the bank. |
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| From D OBC, we have |
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| From D ABC, we have |
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| From (i) and (ii), we get |
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| = 17.32m |
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