Find the angle of elevation, depression and the height of a building from the tip of another building with a distance of 1.2 km.
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2.4CM
To find the angle of elevation or depression and the height of a building from the tip of another building, you will need to use trigonometry, particularly the tangent function.
Here are the steps to find the angle of elevation or depression and the height of the building:
1. Measure the distance between the two buildings. In this case, it is given as 1.2 km.
2. Determine the vertical height between the two buildings. This can be done by measuring the difference in height between the two buildings or by using other means such as surveying or elevation data.
3. Identify the right-angled triangle formed by the two buildings and the line of sight between them. The base of the triangle is the horizontal distance between the buildings (1.2 km), and the height of the triangle is the vertical height between the buildings.
4. To find the angle of elevation or depression, use the tangent function:
tan(theta) = height / distance
Here, theta represents the angle of elevation or depression, height is the vertical height between the buildings, and distance is the horizontal distance between the buildings.
Rearrange the equation to solve for theta:
theta = arctan(height / distance)
Use a calculator that has the arctan (inverse tangent) function to calculate the angle.
5. To find the height of the building, you can use the tangent function again:
tan(theta) = height / distance
Rearrange the equation to solve for height:
height = distance * tan(theta)
Plug in the values of distance and theta to calculate the height.
By following these steps and using the given distance and/or measuring the vertical height between the buildings, you can find the angle of elevation or depression and the height of the building from the tip of another building.