What are the angle of elevation and angle of depression in trignometry?

Answer 1

When you are seeing any object lying above you, the angle made from horizontal through which you need to raise(i.e. elevate) your eyes to see the object is called angle of elevation.
Similarly when an object is below your eye-level, the angle from horizontal throgh which your eyes must be brought down(i.e. depressed) to see the object is called angle of depression.

Answer 2

In a word problem, you may run into an angle described as "elevation" or "depression." It is trying to tell you where the angle lies in the drawing.

For example, you may have someone looking up toward the top of a building, and the angle of elevation is 40 degrees. The problem is telling you the size of the angle--how "far up" (in degrees) the person is looking.

Or you may have someone on a mountain looking down into a valley, and the angle of depression is 40 degrees. This is telling you how "far down" (in degrees) they are looking.

The most important thing--especially with angles of depression--is that they are always measured from the horizontal--NEVER from the vertical. I can't draw here, but let me explain. Suppose we have the guy in a hot air balloon looking down at something on the ground--say he sees a dog. We want to know how far it is from the dog to a point directly beneath the balloon if the angle of depression is 40 degrees and the balloon is 200 feet off the ground.

Now draw a vertical line to represent the height of the balloon--label it 200 ft. At the bottom of that line, draw a horizontal line to the right. Go ahead and label the 90 degree angle (square corner). This represents the distance we are looking for, from directly beneath the balloon to the dog. Draw your hypotenuse--from the top of the vertical line to the end of the horizontal line. We now have a triangle. Where does the 40 degrees go?

Since angles of depression are measured from the horizontal, add one more line to the drawing. At the top of the vertical line, draw a horizontal line extending to the right. This is the horizontal "line of sight" from the balloon. The 40 degree angle of depression is between this line and the hypotenuse--OUTSIDE the triangle.

Using the "alternate interior angles" theorem from geometry (remember that one?), this means that the lower right angle of the triangle is also 40 degrees. Now you have the angle of depression converted to an angle of elevation INSIDE the triangle, and you can solve.

The other way to think about it is at the balloon, there is 90 degrees between the horizontal line and the vertical. If 40 degrees lie outside of the triangle, then 50 degrees must lie inside the triangle. So the upper angle of the triangle is 50 degrees--meaning that the lower right angle is 40 degrees.

Sorry for the long description--but this is the trickiest part of dealing with an angle of depression. You have to measure it from the horizon--never from the vertical.

Answer 3

Angles of elevation and depression are angles that are formed with the horizontal.
If the line of sight is upward from the horizontal, the angle is an angle of elevation;
if the line of sight is downward from the horizontal, the angle is an angle of depression.
These types of angles and some trigonometry can be used to indirectly calculate heights of objects or distances between points. Alternatively, if the heights or distances are known, the angles can be determined.

Answer 4

When an angle is measured in up ward direction with respect to the horizontal line or axis then it is called "ANGLE OF ELEVATION."

When an angle is measured in down ward direction with respect to the horizontal line or axis then it is called "ANGLE OF DEPRESSION"

Angle of elevation and angle of depression are the terms generally used in solving the problems of "height and distance " in trigonometry.

Answer 5

AOE is the upward angle, normally found at the base.
AOD is the downward angle, normally at the top