Answer:
The kite is 35.71 m high from Emily.
Step-by-step explanation:
Supposing that the kite's string is a straight line, Anna, Emily and the kite form a right triangle (see the figure below).
A right triangle follows the Pythagoras' theorem (or Pythagorean theorem):
[tex]\\ a^{2} + b^{2} = c^{2}[/tex], where c is the hypotenuse and a and b, the other two sides (catheti).
Since the opposite side to the right angle (90°) is the hypotenuse, in this case, c = 50 m, and we know that d = 35 m (the distance from Anna to Emily, or vice versa), we can rewrite the equation for this problem as follows (see figure below):
[tex]\\ d^{2} + h^{2} = (50m)^{2}[/tex], or
[tex]\\ (35m)^{2} + h^{2} = (50m)^{2}[/tex]
Likewise, the height h is the unknown value or the height of the kite from Emily (or one leg of the right triangle).
[tex]\\ h^{2} = (50m)^{2} - (35m)^{2}[/tex].
[tex]\\ h = \sqrt{(50m)^{2} - (35m)^{2}}[/tex], which is approximately:
[tex]\\ h = 35.70714 [/tex]m or [tex]\\ h = 35.71 [/tex]m.
That is, the kite is approximately 35.71 m high above Emily.
