I appreciate it!
Hi gobbajeezalus
(Assuming this is a right angled triangle) all unknown angles are available to us from basic properties of triangles so
the unknown angle on the base is 180 - 38 = 142
from that we know the unknown angle in this triangle above is
180 - 142 - 27 = 11
The larger angle for the border triangle is 63 leaving the last unknown angle in the top corner as 52
From there you just use the sine rule to find the hypotenuse of the larger triangle and you can then use pythagoras to find the value for h, basically
sine rule
hyp/sin 142 = 500/sin 11
hypotenuse = 1613feet
pythagoras
sin 27 = h/1613
h = 732.4 feet
Hope thats right