A soccer goal is composed of a pair of 8-foot upright posts positioned 24 feet apart with a horizontal crossbar and netting boxing in the goal. A soccer ball is positioned directly in front of the right goal post. If the ground distance from the ball to the right goal post is 7 feet, what is the ground distance from the ball to the left goal post?

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If we create a triangle where the vertices are the soccer ball, the right goal post and the left goal post we would see that they create a right triangle.  The distance from the ball to the right goal post would be one leg (the altitude) of the triangle.  The distance from the right...

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If we create a triangle where the vertices are the soccer ball, the right goal post and the left goal post we would see that they create a right triangle.  The distance from the ball to the right goal post would be one leg (the altitude) of the triangle.  The distance from the right goal post to the left goal post would be the second leg (the base).  The distance from the ball to the left goal post would be thehypotenuse of the triangle.

Using the notation for Pythagoras' Theorem we would have that

a = 7 ft     b = 24 ft     c =?

To solve for c we would insert the values into Pythagoras's equation:

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or

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The ball is 25 feet from the left goal post.

 

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