Angle of Elevation Calculator

An online angle of elevation calculator is particularly programmed to estimate the angle of inclination of an object located at a certain height with respect to the ground. Now how do you find the height of something? Before you move on, let us make sure that something can be anything. It can be either an object, a car, an aeroplane or even a person standing on a tall building.

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What Is Angle Of Elevation?

In mathematics;

“An angle of an object located at a particular height with respect to the horizontal line of sight is termed angle of elevation”

Real life example:

• A person looking at an aeroplane hat is taking off.
• A baby girl gazing at a cat sitting on a certain height.
• A girl looking at an apple attached to a branch of the tree at a particular height.

Angle Of Elevation Formula:

Determining angle of elevation is very easy. All you need to do is to follow the equation below:

$$ \text{Angle Of Elevation} = arctan(\frac{Rise}{Run}) $$

Our free online measure of angle calculator determines the angle of elevation with the help of the same formula. But before you start calculating angle of elevation, you must keep in mind the following parameters for a proper results.

Rise:

How to find the height of an object? Believe us it is very simple. Please continue reading!

If you rearrange angle of elevation formula, you can easily determine the height of an object as follows:

$$ tan (A) = \frac{\text{Side Opposite To Angle A}}{\text{Side Adjacent To Angle A}} $$

$$ \text{Side Opposite To Angle A} = \text{Side Adjacent To Angle A} * tan (A) $$

$$ Rise = \text{Side Adjacent To Angle A} * tan (A) $$

Run:

You can calculate the run with the help of the equation below:

$$ tan (A) = \frac{\text{Side Opposite To Angle A}}{\text{Side Adjacent To Angle A}} $$

$$ \text{Side Adjacent To Angle A} = \frac{\text{Side Opposite To Angle A}}{ tan (A)} $$

$$ Run = \frac{\text{Side Opposite To Angle A}}{ tan (A)} $$

Grade:

“It is the ratio of rise to run”

$$ Grade = \frac{Rise}{Run} $$

Conversion Of Degrees Into Radians And Vice Versa:

When you want to convert radians into degrees, use the following formula:

$$ θ_{deg} = \text{Angle in Radians} * \frac{180}{π} $$

Similarly, if you wish to convert an angle given in degrees to radians, subject to the equation below:

$$ θ_{rad} = \text{Angle in Degrees} * \frac{π}{180} $$

How To Find Angle Of Elevation?

You can evaluate the inclination angle with the help of our free online angle of elevation calculator. But it is also very important to have hands-on practice on manual computations as well. Do not get worried as we are going to solve a few examples so that you get a firm hold on the procedure.

Example # 01:

An aeroplane flies at a height of 2km above the ground. The horizontal distance from the observer’s point of location to the aeroplane is about 1km. How to find the angle of elevation?

Solution:

We know the angle of elevation formula:

$$ \text{Angle Of Elevation} = arctan(\frac{Rise}{Run}) $$

Putting the values of height and horizontal distance in the above formula:

$$ \text{Angle Of Elevation} = arctan(\frac{2}{1}) $$

$$ \text{Angle Of Elevation} = arctan(2) $$

$$ \text{Angle Of Elevation} = 63.434^{∘} $$

Converting this angle into radians as follows:

$$ θ_{rad} = \text{Angle in Degrees} * \frac{π}{180} $$

$$ θ_{rad} = 63.434^{∘} * \frac{π}{180} $$

$$ θ_{rad} = 63.434^{∘} * \frac{3.14}{180} $$

$$ θ_{rad} = 1.10 rad $$

Now, determining the grade of elevation as follows:

$$ Grade = \frac{Rise}{Run} $$

$$ Grade = \frac{2}{1} $$

$$ Grade = 2 $$

$$ Grade Percentage = 200% $$

Here our free online angle measure calculator determines the same results but in a span of seconds as time is money!

Example # 02:

The angle of elevation from a particular point to the top of the building is about \(23^{deg}\) and the horizontal distance from point A to the bottom of the building is 10m. How to calculate height?

Solution:

$$ tan (A) = \frac{\text{Side Opposite To Angle A}}{\text{Side Adjacent To Angle A}} $$

$$ tan (23^{deg}) = \frac{\text{Side Opposite To Angle A}}{\text{Side Adjacent To Angle A}} $$

$$ 0.424 = \frac{\text{Side Opposite To Angle A}}{10} $$

$$ 0.424 = \frac{\text{Side Opposite To Angle A}}{10} $$

$$ 0.424 * 10 = \text{Side Opposite To Angle A} $$

$$ \text{Side Opposite To Angle A} = 4.24m $$

Example # 03:

How to solve for height of a long tower with inclination angle of \(12^{deg}\) and distance from the point to the ground level of the building be 52m?

Solution?

We know that:

$$ tan (A) = \frac{\text{Side Opposite To Angle A}}{\text{Side Adjacent To Angle A}} $$

Or

$$ Rise = \text{Side Adjacent To Angle A} * tan (A) $$

Putting the values:

$$ Rise = 52 * tan (12) $$

$$ Rise = 52 * 0.212 $$

$$ Rise = 11.024m $$

Here with the help of a construction angle calculator, you can solve such problems in a fraction of seconds without wasting your precious time.

How Online Angle Of Elevation Calculator Works?

Our free angle distance calculator is the most reliable method considered to find the angle of elevation while doing such analysis. What about having a proper guide to use it!

Keep scrolling!

Input:

First of all, select either of the following options from the drop down menu:

• Angle of Elevation
• Vertical Distance (‘rise’)
• Horizontal Distance (‘run’)

After you select any one of the above options:

• Enter the parameters against the selected term
• Hit the ‘calculate’ button

Output:

Our free measuring angles calculator calculates either:

• Angle of elevation in degrees or radians
• Rise in various units of length
• Run in the same units as defined for rise

FAQ’s:

What is height in math?

In mathematics, height is actually the vertical distance from ground level to the most upper floor of a building.

What do you mean by the term trigonometry?

The word tri means “three”, goni means “angle” and metry means ”measurement”. So, trigonometry is the measurement of angles and is a very sensitive branch of mathematics.

Can angle of elevation be greater than \(90^{deg}\)?

No, the inclination angle can never be greater than \(90^{deg}\) but can be smaller or equal to it.

When inclination angle becomes maximum?

An angle of elevation becomes maximum whenever you come closer to the object. And when you move far from the object, it becomes smaller and smaller.

Conclusion:

In the field of architecture and designing, inclination angle is of great significance as it is used to find the heights of tall buildings with the help of trigonometric ratios and formulas. Architectural engineers always prefer to use an online angle of elevation calculator to estimate most accurate angles so that they could make 3D maps. Also, students should have a basic understanding of it before they enter into their professional career of engineering sciences.

References:

From the source of wikipedia: Elevation

From the source of khan academy: Intro to radians, Radian angles & quadrants, Tangent identities

From the source of lumen learning: Trigonometric Functions, Trigonometric Identities, Key Equations