Sin J = cos K
sin J = cos (90 - J)
So, K = 90 - J
Therefore, 60 deg, 30 deg satisfy the condition sin J = cos K.
Let's just start with x=20 and then do some algebra to it to make it all complicated
x = 20
2 * x = 2 * 20
2x = 40
2x - 13 = 40 - 13
2x - 13 = 27
About 12.56 units.
Solve for x by plugging in values into Pythagorean theorem.


Simplify

Subtract 144 from both sides

divide both sides by 2

complete the square

take the square root of both sides.

subtract by 6 to get about 17.28 for x.
Plug in values for x to get distance traveled on outside of the yard.
17.28 + (17.28 +12) = 46.56
subtract 34 from the length to get the difference in travel. 46.56-34=12.56
(opposite angles in a parallelogram)
(subtraction)
(angles in a triangle add to 180 degrees)
(adjacent angles in a parallelogram are supplementary)
(subtraction)
(angles in a triangle add to 180 degrees)
(angles on a straight line add to 180 degrees)