Trigonometry question help?

Refer to the diagram,
where h m is the height of the tower, and x is the distance between the tower and the second point.

In the smaller right-angled triangle :
h/x = tan36°
x = h/tan36° …… [1]

In the greater right-angled triangle :
h / (x + 30) = tan27°
x + 30 = h/tan27°
x = (h/tan27°) + 30 …… [2]

[1] = [2] :
h/tan36° = (h/tan27°) - 30
(h/tan27°) - (h/tan36°) = 30
h [(1/tan27°) - (1/tan36°)] = 30
h = 30 / [(1/tan27°) - (1/tan36°)]
h = 51.2 (to 1 decimal point)
Height of the tower = 51.2 m

Let height of tower = y metres
tan 27⁰ = y / x
tan 36⁰ = y / [ x - 30 ]

x tan 27⁰ = [ x - 30 ] tan 36⁰
30 tan 36⁰ = x [ tan 36⁰ - tan 27⁰ ]
x = 30 tan 36⁰ / [ tan 36⁰ - tan 27⁰ ]
x = 100 • 4 m

y = 100 • 4 tan 27⁰
y = 51 • 2 m

Let x = distance from second point to top tower

h = height of tower

Then

x/sin(27) = 30/sin(9)

x = sin(27) * 30/sin(9)

h/x = sin(36)

h = xsin(36)

h = sin(27) * 30/sin(9) * sin(36)

= 51.17457723

= 51.17 m