Question

Anna has let out 50 meters of kite string when she observes that her kite is directly above emily. If anna is 35 meters from emily how high is the kite?

Answer 1

If you draw a picture you can see that the kite, Anna and Emily form a right triangle.

so you can use the pythagorean theorem to find the answer.


`35 ^(2) + b^(2) = 50^(2)`

1,225 + b^{2} = 2,500

b^{2} = 1,275

b = 35.7 meters

Answer 2

The kite is 35.71 m high from Emily.

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):

`\\ a^(2) + b^(2) = c^(2)`, 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):

`\\ d^(2) + h^(2) = (50m)^(2)`, or

`\\ (35m)^(2) + h^(2) = (50m)^(2)`

Likewise, the height h is the unknown value or the height of the kite from Emily (or one leg of the right triangle).

`\\ h^(2) = (50m)^(2) - (35m)^(2)`.

`\\ h = \sqrt{(50m)^(2) - (35m)^(2)}`, which is approximately:

`\\ h = 35.70714`m or
`\\ h = 35.71`m.

That is, the kite is approximately 35.71 m high above Emily.