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Angles of Elevation and Angles of Depression

Angles of Elevation and Angles of Depression. Definition. Object. Angles of Elevation and Angles of Depression. Angle of Elevation

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Angles of Elevation and Angles of Depression

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  1. Angles of Elevation and Angles of Depression

  2. Definition Object Angles of Elevation and Angles of Depression 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 Angle of elevation Horizontal line

  3. Definition Object Angles of Elevation and Angles of Depression 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

  4. Solving problems involving the angles of elevation and the angles of depression Angles of Elevation and 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.

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

  6. J x N 480 m M 36° 30' h m B 200 m Angles of Elevation and Angles of Depression Calculate the angle of elevation of the helicopter from the peak of the control tower. (b) Solution: 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‘.

  7. Angle of elevation and the corresponding angle of depression are equal The same Angles of Elevation and Angles of Depression Horizontal line Angle of depression Angle of elevation Horizontal line

  8. The End

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