Introduction to Height and Distance

Height and distance have been used for calculating the distances between the celestial bodies, such as from the Earth to the planets in the solar system as well as the stars for decades. Moreover, one of the best examples of the use of height and distance was the determination of the height of the tallest mountain in the world, Mount Everest named after George Everest. However, in recent times, the concept of height and distance is useful in the recognition of marine biology, crime, navigation, military forces, astronomy, calculus, aviation, as well as many other things. Notably, it is also helpful in measuring the height of the pillars, buildings, mountains, historical monuments, etc.

Concept of height and distance

The height and distance of anything can be determined easily with the use of trigonometric formulas. For instance, the height and distance can help in determining the height of the Qutub Minar if you have information on the distance of Qutub Minar from your location as well as the angle at which you can see the top of the Qutub Minar. To find out the height, trigonometry can be used because the surface of the ground, the height of the Qutub Minar as well as the line of elevation all together make a right angle triangle between the Qutub Minar and the ground.

Generally, the distance is the base of the right angle triangle made by the Qutub Minar’s height as well as the line of sight. The length of the horizontal level also determines the distance because it also makes the triangle’s base which is at a specific height; however, it is parallel to the ground. Moreover, the line of sight makes the hypotenuse of the right-angle triangle. In addition, the line that goes perpendicular to the ground makes the triangle’s height.

Terms that relate to height and distance

•   Line of sight – It refers to the straight line which is made from the observer’s eye to an object’s point that is to be viewed.
•   Horizontal level – It refers to the horizontal line which is made from the viewer’s eye.
•   The angle of elevation – It refers to the angle made amid the line of sight as well as the horizontal level in case the object is over the horizontal level.
•   The angle of depression – It refers to the angle made amid the line of sight as well as the horizontal level in case the object is underneath the horizontal level.

Pythagoras theorem

Since the height and distance from a right-angle triangle, the Pythagoras theorem can be used to determine the length of the sides. Moreover, the Pythagoras theorem says that the square of the hypotenuse in a right-angle triangle is equivalent to the total summation of the square of its base as well as height.

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

If the length of the base, perpendicular and hypotenuse in a right angle triangle is ‘a’, ‘b’ and ‘c’ respectively, then:

a2 + b2 = c2

Therefore, if the length of any 2 sides is recognized then the length of the third side can be determined using the Pythagoras theorem, also known as the Pythagorean triple.

Some practical applications of height & distance:

To determine the slope and height at the time of construction

The height of a building or a historical monument can be determined if the distance, as well as the angle of elevation of the structure, is available. In the same way, the angle of elevation, angle of depression, as well as the distance of the structure or an object can be easily determined if other information is available.

To measure the height of a building or any mountain

Generally, the height of any building or a mountain can be easily found with the use of trigonometric ratios. Consider the building’s base as adjacent and the height as the opposite, then the third-longest part of the triangle will be the hypotenuse. Moreover, the triangle should be a right-angle triangle.

Conclusion

This article concludes that the height and distance questions are applicable in real life as well and can be used to find out the distances between various elements. Moreover, the journey in the order of the heights and distances starts with what a learner already knows and keeps on going to productively develop a fresh perception in the minds of the young learners.