Apply the Law of Sines.
sin A sin B sin C
------- = -------- = --------
a b c
Inserting the given data,
sin 36 sin B sin C
--------- = -------- = --------
250 300 420
300 sin 36
Then 300 sin 36 = 250 sin B, and sin B = ---------------- = 0.705
250
Thus, arcsin B = 0.783 rad = 44.857 degrees, or about 45 degrees.
Taking B to be 45 degrees and the given angle 36 deg, then the 3rd angle must be 180 - (45+36) = 99 degrees (which is opposite the 420-ft side).
At this point we apply Heron's formula. You should look this up on the 'Net.
a + b + c 250 + 300 + 420
First, we calculate S = --------------- = ------------------------ = 970/2 = 485
2 2
and then calculate sqrt (S(S-A)(S-B)(S-C):
Area of triangle / lot is then:
A = sqrt(485(485-250)(485-300)(485-420))
= sqrt(485(235)(185)(65) )
= 37021 square feet
