#1) In the sketch, the school is located at coordinates (1, 1). Going north (up) 4 blocks and east (right) 3 blocks to get home places it at (4, 5). The distance formula is:
. Using our coordinates we have:
His house is 5 blocks from the school in a straight line.
#2) The ladder (14 ft) forms the hypotenuse of a right triangle, with the legs being the distance from the house (6 ft) and the height of the ladder (b ft). This gives us:
Subtract 36 from both sides:
Take the square root of both sides:
One possibility for the height of the second story window is 13 feet, since it is longer than 12.6.
#3) The distance from 1st base to 3rd base forms the hypotenuse of a right triangle, with each leg being equal to <em>s</em>, the side length of the square formed by the baseball diamond. Using the Pythagorean theorem we have:
, where <em>d</em> is the distance from 1st to 3rd. Combining like terms gives us
. Taking the square root of both sides we have
(this is due to the fact that square root cancels a squared variable, so <em>s</em> comes out of the radical sign).
#4) The straight distance from the boat's original position to its new position forms the hypotenuse of a right triangle, with the legs being the distance west (600) and the distance south (800) it traveled. Using the Pythagorean theorem we have:
Taking the square root of both sides we have
The straight distance between the two points would be 1000 meters.