Question

A tower that is 65m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59m. What obtuse angle does the tower make with the ground?

Answer 1

I am visualizing something like the Leaning Tower of Pisa.

The statement "A tower is 65 m high" is misleading, since height is measured along a perpendicular.
In the next sentence you say "the vertical distance from the top of the tower to the ground is 59 m"
Thus I will assume that the "length" of the tower is 65 m.
So in effect you have a right angled triangle with hypotenuse 65, and opposite side 59
let the angle at the base be Ø
sinØ = 59/65 = .90769...
Ø = 65.2° making the obtuse angle 114.8°