Small Angle Q.... Please. :) (1 Viewer)

[Smile12345]

Hello All

Could someone please assist me with the following:

'Given that the wingspan of an aeroplane is 30m, find the plane's altitude to the nearest metre if the wingspan subtends an angle of 14' when it is directly over head..."

Thanks in advance.

Smile.

 

[aDimitri]

So what we have is essentially our plane (lets call the wing tips A & B) directly above a point on the ground (lets call this point C). We know that the distance of A to B is 30m, and that the angle that AB subtends at C is 14' (that is, angle ACB = 14').

What we want is the perpendicular distance from C to AB. This is the distance to the midpoint of AB (lets call that point N). SO the distance from A to N is 15m (half of AB), and the angle AN subtends at C is 7' (half of angle ACB). We now have a right angled triangle, one side 15m, one side our altitude (h), and one angle of 7'.
tan(7') = 15/h
h = 15/tan(7')
h ~ 7366.59m

 

[Smile12345]

So what we have is essentially our plane (lets call the wing tips A & B) directly above a point on the ground (lets call this point C). We know that the distance of A to B is 30m, and that the angle that AB subtends at C is 14' (that is, angle ACB = 14').

What we want is the perpendicular distance from C to AB. This is the distance to the midpoint of AB (lets call that point N). SO the distance from A to N is 15m (half of AB), and the angle AN subtends at C is 7' (half of angle ACB). We now have a right angled triangle, one side 15m, one side our altitude (h), and one angle of 7'.
tan(7') = 15/h
h = 15/tan(7')
h ~ 7366.59m

Thanks very much for your clear explanation...

That makes complete sense now... +1 to your rep