Gregor is using 35 feet of spare fencing to build a triangular play pen for his dog. So far, he has constructed two sides that join at a right angle, and one of the sides is 12 feet long. He begins to construct the third side, which is 17 feet long, by attaching the fencing at an angle to the side that is 12 feet long.

Part A: To the nearest degree, what is the angle between the side that is 12 feet long and the side that is 17 feet long?

Part B: What is the length of the second side?

Part C: Will Gregor have enough fencing to complete the triangular pen? Why or why not?

Select one answer for Part A, one answer for Part B, and one answer that correctly answers both questions for Part C.

see the picture attached to better understand the problem

we know that

in the right triangle ABC
AB=12ft (one leg)
BC=17 ft (hypotenuse)
AC=? (second leg)

Applying the Pythagorean Theorem
BC²=AB²+AC²
solve for AC
AC²=BC²-AB²------> AC²=17²-12²-------> AC²=145
AC=12.04 ft
let
B=angle ABC
cos B=AB/BC-----> cos B=12/17
B=arc cos (12/17)------> B=45.10 degrees------> B=45 degrees

The answer part a) is
the angle between the side that is 12 feet long and the side that is 17 feet long is 45 degrees

The answer Part b) is
the length of the second side is 12.04 ft

Part c) Will Gregor have enough fencing to complete the triangular pen? Why or why not?

Find the perimeter of a triangular play pen
P=AB+BC+AC-----> P=12+17+12.04-----> P=41.04 ft
so
41.04 > 35 ft

therefore
Gregor does not have enough fencing to complete the triangular pen

the answer Part c) is
Gregor does not have enough fencing to complete the triangular pen