Answer:
(a) The height of the building is 60.06 m
(b) The distance AB is 139.43 m
Step-by-step explanation:
 The given parameters are
Given that segment BT = segment AT + 29 
By trigonometric ratios, we have;
cos∠ATC = CT/AT
cos∠BTC = CT/BT
Therefore, we have;
cos(40°) = CT/AT.................................(1)
cos(56°) = CT/BT = CT/(AT + 29).....(2)
cos(56°) = CT/(AT + 29)......................(3)
From equation (1)
CT = AT×cos(40°)
From equation (3)
AT×cos(56°) + 29 × cos(56°) = CT
Therefore;
AT×cos(40°) = AT×cos(56°) + 29 × cos(56°) 
AT×cos(40°) - AT×cos(56°) =  29 × cos(56°) 
AT×(cos(40°) - cos(56°)) =  29 × cos(56°) 
AT = 29 × cos(56°)/(cos(40°) - cos(56°)) = 78.4 m
TC = CT = AT×cos(40°) = 78.4×cos(40°) = 60.06 m
The height of the building = 60.06 m
(b) BT = AT + 29 = 78.4 m + 29 m= 107.4 m
AB = AT×sin(∠ATC ) + BT×sin(∠BTC) = 78.4×sin(40°) + 107.4×sin(56°) =  139.43 m
The distance AB =  139.43 m.