The Important of Horizontal line in measuring angle of Elevation and Depression

Remember, we need to measure from the horizontal in order to get the angle of Elevation and Depression. Common mistake is often occur when measuring the angle of Elevation and Depression NOT from the horizontal.






Distance and height; these two play an important role in order to measure whether the angle of Elevation or Depression. In some cases, the situation will give us the information on height and the value of angle, then we need to find the distance and vice versa.

Let us look at the situation below and try to solve by using your own knowledge.

Suppose that we want to find the height of this tree.

We mark point A and what is the distance from the base of the tree.

Then we measure the angle of elevation from A to the top of the tree.

Now,

We have measured and so we can calculate tan() and thus we can find h, which is the height of the tree.

Let's Identify where is the Angle of Elevation and Angle of Depression?

Activity 1

Let say that you as a hiker walking down from the top of the mountain. At one sight, you could observe a peak of another mountain and below you could see a hut. Can you please identify and describe each angle as it relates to the situation above.

Angle 1 : Angle 1 is the angle of ___________ from the ________ to the _________. 

Angle 2 : Angle 2 is the angle of ___________ from the ________ to the _________.
Angle 3 : Angle 3 is the angle of ___________ from the ________ to the _________.

Angle 4 : Angle 4 is the angle of ___________ from the ________ to the _________.

 

ANGLE OF ELEVATION AND DEPRESSION

When you are looking at a plane on sky, sometimes you may think that you can determine the height of a plane on sky, aren’t you?

How about when you are standing on a hill and you are observing a ship at the sea, can you estimate the distance from your position?

Well, that is what we called as angle of elevation when you are looking up to view objects such as plane on sky and angle of depression when you are looking down to see objects like ship on the sea.

Some characteristics of angle of elevation and depression can be known from table below :

Angle of Elevation	Angle of Depression
Angle of elevation is measured when the object is viewed upward.	Angle of depression is measured when the object is viewed downward.
Angle of elevation is always an angle in the right triangle considered for solving the problem	Generally, an angle in the right triangle which is the alternate interior angle of the angle of depression is considered for solving the problem.
When two positions are each viewed from the other position then, the angle of elevation from one point is equal to the angle of depression from the other point, as two angles are alternate interior angles.

ANGLE OF ELEVATION AND DEPRESSION FORMULA

We might use the formula of inverse trigonometric functions if the related lengths are known.

In the right triangle model, if θ is a measure of angle of elevation or depression then,

We can choose either one formula above depending on the known measures in the triangle.