Geometry provides us with an elementary introduction to shapes around us. This branch of maths is useful in mastering shape reasoning. If you ever wonder how math is going to be used in real life, geometry offers the answer most readily. We know that circles, triangles, and rectangles are the 2D figures that we see around most commonly. Another 2D figure, which is a ramification of the triangle is a right triangle. It is one of the most stable structures and has its utility in the fields of carpentry, architecture, etc.

**How right triangles are used in real-life?**

What exactly is a right triangle? If you visualize elaborately, a right triangle is two line segments placed at 90^{o }angle to each other and their free ends are joined by a diagonally oriented segment. This is a shape that we may locate quite effortlessly around us. Staircases when observed from the side may give you an impression of several right angles juxtaposed to each other. Apart from this common example locatable in homes, listed here are the other real-life uses of the right triangles.

**Shadow cast by a tall object:**A tree forms right angle to the land. Its top and the open end of the shadow form the hypotenuse allowing you to visualize the right triangle structure.

**A climbing ladder leaning to the wall:**A slanting ladder to the wall forms right triangle shape where hypotenuse corresponds to the ladder.

**Angles for placing a slab:**Wall mounted shelves are placed on right triangular holding points.

**A person standing at a tower and locating a ball on the land**: The gaze of a person standing on the tower forms the hypotenuse of the right triangle shape whose two vertical and horizontal arms are height of the tower and distance between the tower and ball.

**Solving right triangle and its application in various professions**

Right triangles fit various spheres of our lives like a glove. These geometrical figures have an entire branch of math dedicated to it. We all know it by the name of ‘trigonometry’. Various relationships between the two from the three sides of the right triangle (trigonometric functions) help solve real-life problems various professionals face^{[1]}. Let’s take a look at those.

**1. Carpentry**

Carpenters need to ascertain that the walls are perfectly straight and corners are squares to fit in the elements as a part of the interior designing process. They may apply the Pythagorean theorem that relates the sides of the right triangle to find the required measurements.

**2. Finding height or length**

In architecture, the experts solve right triangle problems to find the required height or length of any structure. This calculation is needed to assure compliance with the building plan.

**3. Navigation**

In navigation, finding the distance of the ship from the shore, or between two ships or other objects can help in finding the probable duration of the tour. It may also help find the safe speed and the suitable maneuvering angles to keep the vessel protected from hits or accidents.

**4. Surveying**

Surveyor uses the trigonometry functions or solves right triangle based problems to estimate the height of a building. Using a total station theodolite (TST), the surveyor finds the exact angle of elevation from a chosen distance.

**5. Astronomy**

Several astronomical calculations like estimating the radius of the Earth or the movement of certain objects in a particular period can be found using the principles and functions of trigonometry. The study of distances between the two astral bodies becomes possible to do by treating the distance as one arm of the right triangle and applying trigonometry principles.

**6. Astronauts and space scientists**

** **Astronauts, during their expedition to space, need to find the characteristics of weather, soil, air pressure, etc. of the places where they cannot visit physically. They use tools like robotic arms for such purposes. With the help of right triangles-based calculations, they can find the correct angle and orientation for maneuvering the robotic arm or other similar tools.

**Teaching right triangles the activity way**

All the examples mentioned above indicate the possibility of teaching right triangles by using activities. High school students have to hone their trigonometry basic skills. Just solving equations and mugging up values of cos, tan and sine may not produce the required outcomes. Better learning is achieved when they get to apply the concepts. Activities based on right triangles help learn by doing.

**A few activities that involve solving right triangles’ variables are:**

**1. Estimating heights of objects using Lego Robot kit**

Lego Robot Kit act as a portable counterpart of the things students may see around. They apply trigonometry principles to estimate the height of various objects given in the kit. On scaling up the measurements received, they can apply the learning to find the heights of buildings, towers, poles, etc.

**2. Estimating boundaries of a plot**

Prepare the model of a landscape with dummy hills, buildings, empty land, etc. Assign a few values to the objects’ distance from each other and contours of the land. By making hypothetical right triangles from the top of the dummy hill, building, etc., students can learn about how to find values of various variables like height, speed, distance, etc.

**3. Parallax activity to guess the distance between stars and sun**

Parallax means the difference in the position of an object when viewed from different points of view. This displacement can create an angle of view, and two arms that resemble a triangle. By using calculators and trigonometric functions’ tables, they can get the idea of the distance between astronomical objects. Moving forth, the distance between two landmarks can also be estimated.

**Conclusion**

Studying right triangles can help students understand how the geometric and trigonometric principles can be applied to solve real-life problems. It is this practical knowledge attained that helps blur the line between bookish knowledge and applied science. So, next time you are done mugging up the definitions and functions’ values, start making hypothetical models and apply various combinations of values to strengthen your learning. It brings fun into the learning hour and makes the study of mathematical concepts more interesting.

**References:**

- Libretexts. (2021, January 2).
*1.3: Applications and Solving Right Triangles*. Mathematics LibreTexts. https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Elementary_Trigonometry_(Corral)/01%3A_Right_Triangle_Trigonometry_Angles/1.03%3A_Applications_and_Solving_Right_Triangles

I am Pratiksha Bhatt, Bachelor of Life Science, and Masters in Management Studies. I have done certification courses in early education counseling. I am a writer, a mother of a child with spelling difficulties which drove me to alternative resources of education like manipulatives and participatory activities. My areas of expertise are learning difficulties, alternative learning methods, and activity-based learning.