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Test 22 of 39

# Height and Distance

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Height and Distance: Height is a measure of vertical distance, either vertical extent (how “tall” something or someone is) or vertical position (how “high” a point is). For example, “The height of that building is 50 m” or “The height of an airplane is about 10,000 m”.

1. Angle of Elevation: Let us consider a situation where a person is standing on the ground and he is looking at an object which is at some height say the top of the building. The line joining the eye of the man with the top of the building is called the line of sight. The angle made by the line of sight with the horizontal line is called angle of elevation. In this figure the line of sight is making an angle θ with the horizontal line. This angle is the angle of elevation.
2. Angle of Depression: Now let us take another situation where the person is standing at some height with respect to the object he is seeing. In this case again the line joining the eye of the man with the bottom of the building is called the line of sight. The angle made by the line of sight with the horizontal line is called angle of depression. In the above figure ‘θ’ is the angle of depression. Note: The angle of elevation is equal to the angle of depression.
• Let the ΔABC is a right angled triangle. Then Sin θ = AB/AC Cos θ = BC/AC Tan θ = AB/BC Cosec θ = AC/AB Sec θ = AC/BC Cot θ = BC/AB