Solution: The outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to the outer angle.

Get:

∠DAC=60 -45 = 15。

CD=50 meters,

Draw a conclusion from sine theorem

CD/sin 15 =AD/sin45。

AD = 50 *√2/(2 sin 15)( 1)

And sin15 = sin (60-45) = (√ 6-√ 2)/4.

Substitute into the formula (1) and simplify.

AD=50(√ 3+ 1)。

In the right triangle ABD:

AB=AD*sin60

=√ 3AD/2

=50√ 3(√ 3+ 1)/2

=25(√ 3+3)

=25*( 1.732+3)

≈ 1 18 (m).

The height AB of Ferris wheel is about 1 18m.