Step-by-step explanation:
right-angled triangle, and law of sine (for any type of triangles) :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and the correlated angles are always opposite from each other.
and we know that the sum of all angles in a triangle is always 180°.
so, the angle at the foot of the radio tower is 90°.
the angle from the top of the shadow to the top of the tower is 78.5°.
so, the third angle (at the top of the tower) is
180 - 90 - 78.5 = 11.5°
and with the law of sine we get
height/sin(78.5) = 64/sin(11.5)
height = 64×sin(78.5)/sin(11.5) = 314.57005... ft
