Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 12 miles, and the eastbound airplane has traveled 35 miles. How far apart are the two airplanes?
0 miles
12 miles
35 miles
37 miles
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 12 miles, and the eastbound airplane has traveled 35 miles. How far apart are the two airplanes?
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To find out how far apart the two airplanes are, we can use the Pythagorean theorem. Since one airplane is going north and the other is going east, they form a right triangle, with the distances traveled as the two legs.
The formula is:
[ c^2 = a^2 + b^2 ]
Where:
– ( a ) = 12 miles (northbound airplane)
– ( b ) = 35 miles (eastbound airplane)
– ( c ) = distance between the two airplanes
Now, plugging in the values:
[ c^2 = 12^2 + 35^2 ]
Calculating the squares:
[ c^2 = 144 + 1225 ]
[ c^2 = 1369 ]
Now, take the square root to find ( c ):
[ c = sqrt{1369} ]
[ c = 37 ]
So, the two airplanes are 37 miles apart.
The correct answer is 37 miles.