Final answer:
The height of the taller building can be calculated by using trigonometric functions to solve for the heights based on the provided 47° angle of depression and the 21° angle of elevation with the known distance of 35m between the buildings.
Step-by-step explanation:
To find the height of the taller building, we need to use trigonometry to calculate heights based on the angles of elevation and depression given. The distance between the two buildings is 35m.
Let's denote the height of the shorter building as H1 and the height of the taller building as H2. From the top of the shorter building, the angle of depression to the base of the taller building is 47°. Using the angle of depression and the distance between the buildings, we can find H1 using the tangent function: tan(47°) = H1/35m.
Similarly, from the top of the shorter building, the angle of elevation to the top of the taller building is 21°. This gives us another equation: tan(21°) = (H2 - H1)/35m.
We now have two equations, allowing us to solve for both H1 and H2 using the given angles. By calculating H1 and H2, we find the height of the taller building.