10 points i guess

look at the picture of a scaffold used to support construction workers. the height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled pr, is shown:

part a: what is the approximate length of rod pr? round your answer to the nearest hundredth. explain how you found your answer, stating the theorem you used. show all your work. (5 points)

part b: the length of rod pr is adjusted to 16 feet. if width pq remains the same, what is the approximate new height qr of the scaffold? round your answer to the nearest hundredth. show all your work. (5 points)

Part A.
Using the Pythagorean theorem,
  PR² = PQ² +QR²
  PR² = (14 ft)² +(6 ft)² = 196 ft² +36 ft² . . . . substitute the given numbers
  PR² = 232 ft² . . . . . . . . . . . . . . . . . . . . . . . .find the sum
  PR = √(232 ft²) ≈ 15.23 ft . . . . . . . . . . . . . take the square root
The length of rod PR is 15.23 ft.

Part B.
Using the Pythagorean theorem,
  PR² = PQ² +QR²
  (16 ft)² = (14 ft)² +QR² . . . . . . . substitute the given numbers
  256 ft² -196 ft² = QR² . . . . . .. subtract 14²
  60 ft² = QR² . . . . . . . . . . . . . . find the sum
  √(60 ft²) = QR ≈ 7.75 ft . . . . . take the square root
The new height QR is about 7.75 ft.