Can trigonometry be used in everyday life?

Trigonometry may not have its direct applications in solving practical issues, but it is used in various things that we enjoy so much. For example music, as you know sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means sound engineers need to know at least the basics of trigonometry. And the good music that these sound engineers produce is used to calm us from our hectic, stress full life – All thanks to trigonometry.

Trigonometry can be used to measure the height of a building or mountains:

if you know the distance from where you observe the building and the angle of elevation you can easily find the height of the building. Similarly, if you have the value of one side and the angle of depression from the top of the building you can find and another side in the triangle, all you need to know is one side and angle of the triangle.

Trigonometry in video games:

Have you ever played the game, Mario? When you see him so smoothly glide over the road blocks. He doesn’t really jump straight along the Y axis, it is a slightly curved path or a parabolic path that he takes to tackle the obstacles on his way. Trigonometry helps Mario jump over these obstacles. As you know Gaming industry is all about IT and computers and hence Trigonometry is of equal importance for these engineers.

Trigonometry in construction:

In construction we need trigonometry to calculate the following:

• Measuring fields, lots and areas;
• Making walls parallel and perpendicular;
• Installing ceramic tiles;
• Roof inclination;
• The height of the building, the width length etc. and the many other such things where it becomes necessary to use trigonometry.

Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles.

Trigonometry in flight engineering:

Flight engineers have to take in account their speed, distance, and direction along with the speed and direction of the wind. The wind plays an important role in how and when a plane will arrive where ever needed this is solved using vectors to create a triangle using trigonometry to solve. For example, if a plane is travelling at 234 mph, 45 degrees N of E, and there is a wind blowing due south at 20 mph. Trigonometry will help to solve for that third side of your triangle which will lead the plane in the right direction, the plane will actually travel with the force of wind added on to its course.

Trigonometry in physics:

In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. Even in projectile motion you have a lot of application of trigonometry.

Parallelogram (Coordinate Geometry)

 

A quadrilateral with both pairs of opposite sides parallel and congruent, and whose location on the coordinate plane is determined by the coordinates of the four vertices (corners).

Try this Drag any vertex of the parallelogram below. It will remain a parallelogram and its dimensions calculated from its coordinates. You can also drag the origin point at (0,0).

In coordinate geometry, a parallelogram is similar to an ordinary parallelogram (See parallelogram definition ) with the addition that its position on the coordinate plane is known. Each of the four vertices (corners) have known coordinates. From these coordinates, various properties such as its altitude can be found.

It has all the same properties as a familiar parallelogram:

• Opposite sides are parallel and congruent
• The diagonals bisect each other
• Opposite angles are congruent

See parallelogram definition for more.

Sides and diagonals

The lengths of the four sides and two diagonals can be found by using the method described in Distance between two points to find the distance between point pairs.

For example, in the figure above click 'reset' and select "show diagonals' in the options menu. Using the method in Distance between two points, the diagonal AC is the distance between the points A and C:

Diagonal AC

=

√

(

48

−

6

)

2

+

(

26

−

7

)

2

=

46.1

Similarly the side AB can be found using the coordinates of the points A and B:

Side AB

=

√

(

18

−

6

)

2

+

(

26

−

7

)

2

=

22.5

Altitude

The altitude of a parallelogram is the perpendicular distance from a vertex to the opposite side (base). In the figure above select "Show Altitude" in the options menu. It will show the altitude from B to the opposite side AB.

The calculate the length of an altitude, we need to find the perpendicular distance from a point to a line. In the above figure we need the distance from B to the line AD.

Applications of Trigonometry in Real life

Applications of Trigonometry in Real life

• Trigonometry is commonly used in finding the height of towers and mountains.

• It is used in navigation to find the distance of the shore from a point in the sea.

• It is used in oceanography in calculating the height of tides in oceans

• It is used in finding the distance between celestial bodies

• The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

• Architects use trigonometry  to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles