the angle of depression of the top and bottom of an 8m tall building from the top of a multi storyed buiding are 30degree and 45 degree respectively find the height of the multi storyed building and the distance between 2 buildings
Let the height of the multistory building be y and the distance between them be x. The draw yourself a figure.
You should be able to convince yourself that
y/x = tan 45 = 1
(y-8)/x) = tan30 = 0.5774 = (x-8)/x
1 - (8/x) = 0.5774
8/x = 0.4226
x = 18.9 m
y = 18.9 m
To find the height of the multi-story building and the distance between the two buildings, we can break down the problem into two separate parts:
1. Finding the height of the multi-story building:
Let's assume the height of the multi-story building is 'h' meters.
Using the angle of depression of 30 degrees, we can form a right-angled triangle with the top of the multi-story building, the bottom of the 8m tall building, and a line of sight connecting the two.
sin(30) = (8m) / (h)
h = (8m) / sin(30)
By substituting the value of sin(30) as 1/2, we get:
h = (8m) / (1/2)
h = 16m
Therefore, the height of the multi-story building is 16 meters.
2. Finding the distance between the two buildings:
Let's assume the distance between the two buildings is 'd' meters.
Using the angle of depression of 45 degrees, we can form a right-angled triangle with the top of the multi-story building, the bottom of the 8m tall building, and a line of sight connecting the two.
tan(45) = (8m) / (d + 8m)
By substituting the value of tan(45) as 1, we get:
1 = (8m) / (d + 8m)
d + 8m = 8m
d = 0m
Therefore, the distance between the two buildings is 0 meters.
Please note that it is not possible to have a distance of 0 meters between two buildings in this scenario. It is likely that there might be an error in the given information or the measurements.