The angle of depression from the top of a 320 foot office building to the top of a 200 foot office building is 55degrees. How far apart are the two buildings?
Draw a picture
Tangent(35) = d/120 making
d = 120(tan35)
..........or
tan(55) = 120/d making
d = 120/tan55.
First one
Jsjsj
To find the distance between the two buildings, we can use trigonometry and specifically the tangent function.
First, let's define the problem. We have two buildings, one with a height of 320 feet and the other with a height of 200 feet. The angle of depression is given as 55 degrees.
Now, let's draw a diagram to better visualize the situation. Imagine a horizontal line representing the ground and two vertical lines representing the buildings. We have an angle of depression from the top of the taller building to the top of the shorter building.
| |
| |
| 320 ft
| |
------------------------ Ground
| |
| 200 ft
| |
| |
According to the diagram, we have a right-angled triangle, where the angle of depression (55 degrees) is opposite to the shorter side (200 ft) and adjacent to the longer side (the distance we want to find).
Since we have the ratio of the opposite side to the adjacent side (the height of the shorter building to the distance between the two buildings), we can use the tangent function:
tan(angle) = opposite / adjacent
In this case, the tangent of the angle of depression (55 degrees) is equal to the height of the shorter building (200 ft) divided by the distance between the two buildings (unknown).
So, we can set up the equation:
tan(55 degrees) = 200 ft / distance
To solve for the distance, we need to isolate it. We can start by multiplying both sides of the equation by the distance:
distance * tan(55 degrees) = 200 ft
Next, divide both sides by tan(55 degrees):
distance = 200 ft / tan(55 degrees)
Now, we can calculate the distance using a calculator:
distance = 200 ft / tan(55 degrees)
distance ≈ 185.55 ft
Therefore, the two buildings are approximately 185.55 feet apart.