The angle of elevation from the top of a 10m high building to the top of a taller building is 12°. The angle of depression from the top of the 10m building to the bottom of the taller one is 37. How tall is the taller building
It depends on the distance between the buildings.
indan mathmatics history
12.82 m
To find the height of the taller building, we can use trigonometry. Let's label the height of the taller building as 'h'.
First, let's consider the angle of elevation. The angle of elevation is the angle between the horizontal ground and the line of sight from the top of the 10m building to the top of the taller building. In this case, the angle of elevation is 12°.
Using trigonometry, we can use the tangent function to relate the angle of elevation with the height of the taller building:
tan(angle of elevation) = opposite/adjacent
tan(12°) = h/10
Now, let's consider the angle of depression. The angle of depression is the angle between the horizontal ground and the line of sight from the top of the 10m building to the bottom of the taller building. In this case, the angle of depression is 37°.
Using trigonometry again, we can utilize the tangent function to relate the angle of depression with the height of the taller building plus the height of the 10m building:
tan(angle of depression) = opposite/adjacent
tan(37°) = (h + 10)/10
Now we have a system of two equations:
tan(12°) = h/10
tan(37°) = (h + 10)/10
Solving this system of equations will give us the value of 'h', which represents the height of the taller building.