Answer:
height = 166.96 feet
Note: Here (eq. 1) and (eq. 2) are representing equation 1 and equation 2.
Step-by-step explanation:
Let the height AB = h feet and BC = x feet
In △ABC
tan63° = AB/BC = h/x
x = h / tan63° .........(eq. 1)
In △ADC
tan49° = AB / (DC + BC) = h / (60 + x)
60 + x = h/tan49° ........(eq. 2)
From (eq. 1) and (eq. 2)
60 + h/tan63° = h/tan49°
60 = h(1/tan49° - 1/tan63°)
60 = h(tan63° - tan49°)/(tan49°*tan63°)
h = 60*tan49°*tan63° / (tan63° - tan49°) = 60*1.15*1.96 / (1.96 - 1.15) = 135.24/0.81 = 166.96 feet
Thus, the height of the building = 166.96 feet