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two birds start flying from the tops of two towers 50 feet apart; one tower is 30 feet high and the other 40 feet high. starting at the same time and flying at the same rate, the birds reach a fountain between the bases of the towers at the same moment. how far is the fountain from each tower?

Sagot :

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Answer:30^2+32^2=40^2+18^2

Step-by-step explanation:

(THIS IS NOT MY ANSWER, I HAVE GOTTEN THIS FROM A LOVELY PERSON NAMED Boreal)

You have to draw this.

The towers are 50 feet apart.  To reach a spot between them, the birds have to fly from the top to a point between them.  There is a right triangle, and the hypotenuses have to be equal.

The bird on the shorter triangle is part of a triangle with the tower 30 and the distance x to the fountain.  They square to 900 + x^2.

The other bird on the 40 foot tower has a distance to the fountain on the ground of 50-x, because the towers are 50 feet apart.

That squares to 2500-100x+x^2.

These must be equal.

2500-100x+x^2+1600=900+x^2

4100-100x=900

-100x=-3200

x=32 feet from the shorter tower and 18 feet from the larger tower.

Therefore 30^2+32^2=40^2+18^2

I know it looks confusing as heck but there is your answer :)

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