Answers:
height of building A = 64 meters
height of building B = 87 meters
=====================================================
Explanation:
Refer to the diagram below.
I have added points A,B,C,D to help find the heights needed.
Focus on triangle BAC. This is a right triangle with 58 degrees as one of the known acute angles (angle BAC = 58). Also known is the adjacent side AB = 40. The unknown side we're after is side BC
------------------
tan(angle) = opposite/adjacent
tan(angle BAC) = BC/AB
tan(58) = BC/40
40*tan(58) = BC
BC = 40*tan(58)
BC = 64.013381161642
BC = 64 meters approximately
This is the approximate height of building A
---------------------
Now focus on triangle DAB
This is another right triangle. The acute angle is now 30 degrees as this is the angle of elevation.
tan(angle) = opposite/adjacent
tan(angle DAB) = DB/AB
tan(30) = DB/40
40*tan(30) = DB
DB = 40*tan(30)
DB = 23.094010767585
DB = 23 meters approximately
Add this onto BC to get
DC = DB+BC
DC = 64+23
DC = 87
Building B has a height of roughly 87 meters
--------
note: a more accurate value would be
DC = DB+BC
DC = 40*tan(30) + 40*tan(58)
DC = 87.107391929227
but when we round this to the nearest meter, we still get DB = 87
