Q6 of 12 Page 203

An aircraft is flying at a constant height with a speed of 360 km/hr. From a point on the ground, the angle of elevation at an instant was observed to be 45°. After 20 sec. the angle of elevation was observed to be 30°. Determine the height at which the aircraft is flying (√3 + 1) km or 2.732 km.

The figure is given below:



Let aircraft fly at a constant height of y km


and let the distance from a point to the starting point of jet bet x km.


Thus, BD = EC = y km


And, AB = x km


As distance = speed × time.


Distance taken by craft to travel from D to E


Using Trigonometry;


∠ DAB = 45°


∠ EAC = 30°


BC = AC – AB = 2 km


⇒


⇒


⇒


⇒ = 2.732 km


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4

The angle of elevation of a jet fighter from a point A on the ground is 60° . after a flight of 15 seconds the angle of elevation changes to 30° .if the jet is flying at the speed 720 km/h find the constant height at which the jet is flying.

 5

An aeroplane at an altitude of 200 m observes the angle of depression of opposite points on the banks of a river to be 45° and 60°. Find in metres the width of the river.

 7

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 8

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