First let's check angle of elevation definition

Now let us define angle of elevation and elaborate it. It is the angle above the x-axis i.e. horizontal that an observer makes while looking at some target. The figure given below explains the angle of elevation definition and related concepts in detail.
angle of elevation

As shown in the diagram above, an observer is looking at an object located above the horizontal axis. In this process, it makes an angle θ with the x-axis. This angle is called angle of elevation.

Understanding the angle of elevation formula:

The angle of elevation formula helps to solve the angle of elevation problems very easily. As it is visible from the figure, the vertical from object makes an right angle with the horizontal. So if we know the height of the object and the linear distance, we can easily find out the angle θ by trigonometric formula. It is given by tanθ = Height / distance. The angle of elevation of the sun that is better known as altitude angle, can also be found by the same method.

Solving angle of elevation problems:

The angle of elevation problem specified below helps understanding the topic and gives a clear idea of practical conditions.

(1) Find the angle of elevation if height of the object is 50 m and is at a distance of 50m.

We know that tanθ = height / distance = 50 / 50 = 1 => θ = tan-11 = 45°.

(2) Find the height of an object that makes an angle of elevation of 60° and is at a distance of 100 m:

From the formula, tangent of the elevation angle is given by tanθ = height / distance => tan 60 = H / 100 => H = 100 x √3 = 100 x 173.2. Thus the height of the object will be around 173.2 m.

Thus we have solved some of the angle of elevation word problems that can be applied to any practical scenarios for finding necessary parameters.

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