Final answer:
The height of the building is calculated using the angle of elevation of 45 degrees to be 120 meters, and the height of the tower is calculated using the angle of elevation of 30 degrees to be approximately 69.28 meters.
Step-by-step explanation:
To calculate the height of the building and the height of the tower, we need to use trigonometry. Since the angle of elevation from the roof of the building to the top of the tower is 30 degrees, and the buildings are 120m apart, we can set up a right triangle with the building as one side, the distance between the building and the tower as the base, and the line of sight as the hypotenuse.
Using the trigonometric ratio of tangent (tan), which is opposite over adjacent, for the 30-degree angle we get:
tan(30) = Height of the Tower / 120m
Solving for the Height of the Tower gives us:
Height of the Tower = 120m * tan(30) = 120m * (\sqrt{3}/3) = 40\sqrt{3} meters
Similarly, using the angle of elevation of 45 degrees from the base of the tower to the roof of the building, we get:
tan(45) = Height of the Building / 120m
Solving for the Height of the Building gives us:
Height of the Building = 120m * tan(45) = 120m * 1 = 120 meters
Therefore, the height of the building is 120 meters and the tower is approximately 69.28 meters tall (assuming 40\sqrt{3} is approximated to 69.28).