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**Angles of Elevation and Angles of Depression**

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**Angles of Elevation and Angles of Depression**

Definition Angle of Elevation = angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated above the horizontal line Object Angle of elevation Horizontal line

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**Angles of Elevation and Angles of Depression**

Definition Angle of Depression = angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated below the horizontal line Horizontal line Angle of depression Object

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**Angles of Elevation and Angles of Depression**

Solving problems involving the angles of elevation and the angles of depression At a particular instant, a helicopter is situated at a height of 480 m vertically above a fire engine. The distance of the fire engine from the foot of a control tower is 200 m. The angle of depression of the fire engine from the peak of the control tower is 36° 30'. Calculate the height of the control tower, the angle of elevation of the helicopter from the peak of the control tower.

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**Angles of Elevation and Angles of Depression**

Calculate the height of the control tower. Solution: In ∆BNM, tan BMN = Sketch a diagram using all the given information. 480 m 36° 30' B M J N x h m 200 m tan 36° 30' = h = 200 × tan 36° 30' = 200 × 0.74 = 148 m The height of the control tower is 148 m.

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**Angles of Elevation and Angles of Depression**

(b) Calculate the angle of elevation of the helicopter from the peak of the control tower. Solution: 480 m 36° 30' B M J N x h m 200 m JN = 480 – 148 = 332 m In ∆JMN, tan x = = = 1.66 x = 58° 56' The angle of elevation of the helicopter from the peak of the control tower is 58° 56‘.

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**Angles of Elevation and Angles of Depression**

Angle of elevation and the corresponding angle of depression are equal Horizontal line Angle of depression The same Angle of elevation Horizontal line

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