i have attempted the following problem but my answers differs from authors and would apreciate if any1 can assist, i do not need the exact method but only to know wether my method is utterly wrong...

standing at the top of a 150ft bulding , an observer angle of depression to the top of a smaller building is 12 degrees, and 34 degrees to the base of the smaller building, thus find the height of the smaller building.

my answer give the smaller building heigh as 120 ft, whereas by the authors if 102.7 ft

solved it by tan 46=opposite/adjacent= tan 46=150/adjacent= solving for the adjacent =144.85

then using the adjacent with the triangle with the vertex at 12 degrees i attempted to fin the opposite which i could use to deduct from the 150 ft to obtain the difference in height.

this give tan 12=opposite/144.85 solving for the opposite=30.78 ft

which i deduct from the height of the tallest building to obtain the difference of height...but so far no joy