One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 ◦ , with a possible error of ± 1 . 2%, what is the error and percentage error?

Question

Use differentials to estimate the error in computing the length of the hypotenuse and what is the percentage error?

Answer 1

20+/-1.2%= (20(.988), 20(1.012))

=(19.76,20.24)

margin of error= 0.24 cm

relative error = 1.2%

hypotenuse =2(20)= 40 cm, in the interval (39.52, 40.48)

side opposite 30 degrees = half the hypotenuse

margin of error= 0.48 cm

relative error= 1.2%