Answer problems in a separate sheet of paper. Please show all your work neatly. You will work with a partner but each of you will need to turn in your own project. Leaning Tower of Pisa PISA, Italy - Workers began removing two sets of steel suspenders attached to the leaning Tower of Pisa on Tuesday, in one of the final phases of a bold plan to partially straighten the famously tilted monument. The 340-foot-long cables had been recurred to the tower in 1998 as a precaution is case it needed to be yanked back up while the soil under its foundation was being excavated. Anchored to giant winches dug into the ground about 100 yards from the tower, the suspenders haven\'t been needed Removal of the suspenders will be completed in time from an inauguration ceremony of the newly straightened tower scheduled for June 16, said Paolo Heiniger, who oversees the project. The tower was closed to the public more than a decade ago, when officials feared it was beginning to lean so much that it might topple over. Work to spot the tower\'s increasing tilt has taken far longer than planned, but officials expect it to be open to tourists in the fall. When work began, the tower leaned 6 degrees, or 13 feet, off the perpendicular on its south side. By removing a small amount of soil, the tower has settled better and now leans about 16 inches less-nearly the tilt it had 300 years ago. The decrease in lean is not enough for the naked eye to detect but sufficient to stabilize the monument, experts have said. Use the fact that the tower was 184.5 feet tall when it stood upright to answer the following questions: The article states that when work began the tower leaned 6 degree or 13 feel, off the perpendicular Draw a sketch and label the two measurements. How high is the tower with a lean of 6 degree ? The article goes on to say that the tower now leans 16 inches less. What is the height of the tower with this lean? **Comment on the fact that while sin 4 degree = 13/184.5 = 0.07046, while sin 6 degree = 0.10453 Can you reconcile this seeming discrepancy?
According to given problem we have length of cable = 340 feet
The length of the cable = 340 feet
Anchored at distance = 100 yards from the tower = 300 feet from the tower
so after this we will get ,
the tower was 184.5 feet tall when it
stood upright. let it be the hypotenuse of the triangle = 184.5 feet
so if the tower leaned 6 degrees so x = 6 Degrees
the tower leaned 13 feet so the opposite side = 13 feet
cos 6 = adjacent side / the leaning tower\'s height
actual height = 184.5 * cos 6 = 183.489 feet
now 16 inch = 1.3 feet
so the new lean = 13 - 1.3 feet = 11.67 feet
now after this we will find
The length of the tower it means the hypotenuse does not change = 184.5 feet
sin ( new angle ) = opposite / hypotenuse = 11.6666667 / 184.5 = 0.063233
new angle = arcsin(0.063233) = 3.6degrees
finally we will get
The new height is the vertical height of the tower that is the adjacent side of the triangle
h2 = cos(3.6) * hypotenuse = cos(3.6) * 184.5
= 184.14 feet answer
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