Estimate of the height Here is a diagram of the measurements we just carried out. The height y of the Green building is given by y=h+xtan(9}. Below is a table of the measurements made, as well as the error in each term. Quantity Variable Measurement Error Height to Jen's eyeball h 4.9 feet :I: .01 feet Distance to Green Building x 175 feet : 3 feet Angle 9 57 degrees :I: 3 degrees Where is the error coming from? - The error in the measurement of Jen's height comes from rounding error and inherent error in using a tape measure to enough accuracy. - The error in the distance to the Green building is coming from a few places: error in the actual length of the rope which may differ by a few inches, error in our walking in a perfectly straight line as we measure, and error coming from the fact that the rope is stretching when we pull on it. lengthening the rope. So in fact, we expect our measurement is likely an overestimate. - The error in the angle is coming from wind and the string not hanging straight down. error in the construction of the device, and error in holding the device to read the measurement. Height estimate 1 point possible [graded] What is the estimated height of the Green Building? (Enter an integer with 3 significant figures.) feet Error in estimate What is Ay, which is an error term representing the difference between the height that we calculated for the building from our measurements and its true height? First note that what we really have is the following. ev+0 - - - - htah X+AX And tan (0 + A0) = (3 + Ay) - (h+ Ah) (5.15) c+ Ax = Ay - Ah+(y - h) (5.16) x + Ax Ay - Ah + x tand = (5.17) c + Axyh The last line uses the fact that tan (6) = a: To determine the error, we solve for Ag: Ag 2 Ah + {x + Am) (tan(l9+ A9 ztanw]. To get a sense of the order of this error term, let's find a linear approximation of tan (9 i A9) near I9 = 57 degrees. Linear approximation of tan 1 point possible [graded] tan