Ava is in a hot air balloon that has just taken off and is floating above its launching point. Mary is standing on the ground 4 meter away from the launching point. If ava and mary are 5 meters apart, how high up is ava ?

Ava's altitude is 3 meters.

Step-by-step explanation:

The position of Ava and Mary can be described by the sides of a right angled triangle. Let Ava's altitude be represented by x.

So that applying the Pythagoras theorem, we have;

= +

= +

25 = 16 +

= 25 - 16

   = 9

x =

   = 3

x = 3 meters

Thus, Ava's altitude is 3 meters.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584