A wall 12 feet long makes a corner with a wall that is 14 feet long. The other ends of the walls are about 18.44 feet apart. Do the walls form a right angle? Explain.
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A wall 12 feet long makes a corner with a wall that is 14 feet long. The other ends of the walls are about 18.44 feet apart. Do the walls form a right angle? Explain.
To determine if the walls form a right angle, we can use the Pythagorean theorem. According to the theorem, if a triangle has sides of lengths ( a ), ( b ), and ( c ) (where ( c ) is the hypotenuse), the relationship is ( a^2 + b^2 = c^2 ).
Here, we have:
– One wall is ( 12 ) feet (one leg of the triangle, ( a )).
– The other wall is ( 14 ) feet (the other leg of the triangle, ( b )).
– The distance between the ends of the walls is ( 18.44 ) feet (the hypotenuse, ( c )).
First, we calculate ( a^2 + b^2 ):
( 12^2 + 14^2 = 144 + 196 = 340 ).
Next, we calculate ( c^2 ):
( 18.44^2 approx 339.6336 ).
Now, we compare ( a^2 + b^2 ) and ( c^2 ):
– ( 340 ) (from the two walls) is not equal to ( 339.6336 ) (from the distance).
Since ( a^2 + b^2 ) does not equal ( c^2 ), the walls do not form a right angle.
In conclusion, the walls do not