By using the concept of Pythagoras Theorem, the result obtained is
Distance between their tops is 13 ft.
What is Pythagoras Theorem?
Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of perpendicular and base.
The figure has been attached
Let the poles be represented by CD and AE and let AC represents the distance between their tops
Construction
A line from C parallel to DE (shown by a dotted line) is drawn
CD = 10 ft.
AE = 15 ft.
BE = 10 ft.
AB = AE - BE
= 15 - 10
= 5 ft.
DE = 12 ft.
BC = 12 ft.
[tex]\angle AED = 90^{\circ}[/tex] [ Angle between pole and ground is 90°]
[tex]\angle ABC = 90^{\circ}[/tex] [ Corrosponding angles are equal]
By Pythagoras Theorem,
[tex]AC^2 = AB^2+BC^2\\AC^2 = 5^2 + 12^2\\AC^2 = 25 + 144\\AC^2 = 169\\AC =\sqrt{169}\\[/tex]
AC = 13 ft.
Distance between their tops is 13 ft.
To learn more about Pythagoras Theorem, refer to the link-
https://brainly.com/question/343682
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