Applications of Trigonometry

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The line of sight is an imaginary straight line drawn from the eye of an observer to the point on the object being viewed. It forms the hypotenuse in most height and distance problems.

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The angle of elevation is the angle formed between the line of sight and the horizontal line when the object being observed is above the horizontal level. It occurs when we raise our head to look at a

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The angle of depression is the angle formed between the line of sight and the horizontal line when the object being observed is below the horizontal level. It occurs when we lower our head to look at

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1. All objects (towers, trees, buildings, etc.) are considered as linear for mathematical convenience 2. Angles of elevation or depression are measured with reference to the horizontal line 3. The hei

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Using tan 60° = opposite/adjacent = height/8 tan 60° = √3 √3 = h/8 h = 8√3 meters Therefore, the height of the pole is 8√3 meters.

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Using sin 45° = opposite/hypotenuse = 500/distance sin 45° = 1/√2 1/√2 = 500/x x = 500√2 meters Therefore, the distance from helicopter to person is 500√2 meters.

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Use the tangent ratio: tan θ = opposite/adjacent This is commonly used in height and distance problems where you know the horizontal distance and need to find the height.

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Use the sine ratio: sin θ = opposite/hypotenuse This is useful when you know the height and need to find the direct distance to an object.