Answer: The height of the taller building is 320 meters
Step-by-step explanation: Please refer to the attached picture for details.
The two buildings have been illustrated in the picture attached as points A and E. The distance between them is line BE which is 24.5 m.
The height of the shorter building which is ED and also equal to BC is given as 40 m.
Looking up at the top of the taller building which is point A an observer forms an angle of elevation of 85 degrees which is angle AEB.
We shall begin by solving for distance AB in triangle ABE. The line AB also marked as e is the opposite, while the line BE which is 24.5 is the adjacent. Hence;
Tan 85 = Opposite/Adjacent
Tan 85 = e/24.5
Tan 85 * 24.5 = e
11.43 x 24.5 = e
280.035 = e
e ≈ 280
Our result shows that from the top of building E, building A measures approximately 280 metres. Having in mind that the taller building (line AC) includes the height (line BC) of the shorter building, building A now becomes,
AC = Line BC + Line AB (that is e)
AC = 40 + 280
C = 320 meters
Therefore the height of the taller building is 320 meters
