Maths 6. Application of Trigonometric Ratios

First show them an example for what purpose is triangle's ratio is studied:

Draw a triangle on board:

Step 1

Tell students this problem:

One comes from masjid and walks 10 meters looks at the top of minar in 45 degree.

Ask them what would be the height of minar?

Take part in their discussion as follows:

                We know only the distance from masjid but not both of the height or hypotenuse.

                And we know that the angle is 45 degree.

                We now want to know the height of minar.

Let a triangle be formed in this case named ABC

Let AB be the distance he walked

Let BC be the height

Let AC be the hypotenuse

Step 2

                List what we know.

                AB= 10m

                BC = Not given

                AC= Not given

                Angle at A = 45 degree

We want to know length of BC

Can any of the trigonometric ratios help us in this case?

….. ?

Step 3

Take a ratio that includes what we know and what we don’t know.

In this case we have to know BC, and we know AB i.e. altitude and base respectively.

So a ratio including these two is Tan

Tan of 45 degree is 1 i.e. BC/AB should be equal to 1

If AB is 10m then BC also should be 10m.

So height of minar is 10m + height of that student.

Their doubt is now that how is the angle measured?

Not so hard…

There are many ways to find out this. Simply take a protractor to eye and look to the top of minar through any line of protractor (This method is simple but cannot be so correct) 

Step 4

                Tell them that in many cases we measure the height, depth, distance, width, length by trigonometric ratios. Such as to measure at what height is an aero plane is flying or what is the depth of sea in a specific location, etc.