Distance, Slopes, and Height
I do not understand why not using the theorem of Pythagoras to calculate the heighth of an object, which yields ways more exactness.
Be a the heighth of the object (here Avatar). You get b and c using the spyglass. a=sqrt(-b^2+c^2) . If 160m horizontally away from the avatar, the spyglass will show you a distance to the top of ca. 165 (164.924) m. Angle alpha can be computed as sin^-1(a/c).