Homework SourseThe measurement of the hypotenuse of a triangle is known to
The measurement of the hypotenuse of a triangle is known to be exactly 20 in. If the length of the shorter leg is measured to be 12 in with a possible error of 0.02 in, use differentials to approximate the error in computing the length of the longer leg. please show work.
Solution
a = 20 in, x = (12.00 ± 0.02) in,
the length of the longer leg = y = (a2 - x2)
dy = -x/(a2 - x2) dx = -12/(202 - 122) * 0.02 = -0.015
y 0.015
