Explanation:
1.
that creates a right-angled triangle :
the string is the Hypotenuse (the baseline, which is the side opposite of the 90° angle).
the invisible "line" from the kite straight down to the ground is one leg. and we need that length.
and the invisible "line" on the ground between the point where Brian is standing, and the point, where the : line: coming down from the kite hits the ground, is the second leg.
the angle between both legs is 90°.
so, we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and the associated angles are always opposite of each other.
in our case, the Hypotenuse (the string) is opposite of 90°.
and the angle opposite of the kite height line is the designated angle of elevation at the point, where Brian is standing : 70°.
so, we have here
65/sin(90) = height/sin(70)
height = 65×sin(70)/sin(90)
sin(90) = 1
height = 65×sin(70) = 61.08002035... m
2.
another right-angled triangle.
what is not clear to me : what does "distance from plane to building" mean ?
is it really the line of sight from the plane in the air to the building in the ground ? which is the Hypotenuse of that triangle.
or is it the ground distance (from the point where the height line hits the ground to the building) ? which is also the air distance (parallel line to the ground distance up in the air with the plane).
remember, the sum of all angles in a triangle is always 180°.
per law of sine we have
height/ sin(28) = line of sight / sin(90) =
= air (or ground) distance / sin(180-28-90)
1200/sin(28) = line of sight / 1 =
= air distance / sin(62)
line of sight (if that is what we need) =
= 1200/sin(28) = 2,556.065362... m
air distance = 1200×sin(62)/sin(28) = 2,256.871758... m
3.
another right-angled triangle.
the Hypotenuse is the line of sight from the point 12 ft away in the ground to the top of the pole.
the ground distance (12 ft) is one leg.
the pole (and its height) is the second leg.
so, we have our law of sine
height/sin(53) = line of sight / sin(90) =
= ground distance / sin(180-53-90)
we need the height, so
height/sin(53) = ground distance / sin(37)
height = 12×sin(53)/sin(37) = 15.92453786... ft