FIND TRIGONOMETRIC RATIOS USING RIGHT TRIANGLES

About "Find trigonometric ratios using right triangles"

Find trigonometric ratios using right triangles :

To find all trigonometric ratios from the given right triangles, first we have to name the sides as hypotenuse side, opposite side and adjacent side. 

Hypotenuse side :

The side which is opposite to 90 degree is known as hypotenuse side.

Opposite side :

The side which is opposite to θ is known as opposite side

Adjacent side :

The remaining the unnaming side is known as adjacent side.

Generally we have 6 trigonometric ratios, those are sin θ, cos θ, tan θ, cosec θ, sec θ and cot θ.

based on the side we have different formula for all above trigonometric ratios.

sin θ = Opposite side/hypotenuse side

cos θ = Adjacent side/hypotenuse side

tan θ = Opposite side/Adjacent side

cosec θ = Hypotenuse side/Opposite side

sec θ = Hypotenuse side/Adjacent side

cot θ = Adjacent side/Opposite side 

Let us see some example problems based on the above concept.

Example 1 :

From the following diagrams, find the trigonometric ratios of the angle 

Solution :

From the above triangle, we come to know that the right angled at B.

AC - hypotenuse side = 10

AB - opposite side = 6 

BC - Adjacent side = 8

sin  θ = Opposite side/Hypotenuse side 

  =  AB/AC ==> 6/10 ==> 3/5

cos θ = Adjacent side/Hypotenuse side 

  =  BC/AC ==> 8/10 ==> 4/5

tan θ = Opposite side/Adjacent side 

  =  AB/BC ==> 6/8 ==> 3/4

cosec θ = Hypotenuse side/Opposite side

  =  AC/AB ==> 10/6 ==> 5/3

sec θ = Hypotenuse side/Adjacent side

  =  AC/BC ==> 10/8 ==> 5/4

cot θ = Adjacent side/opposite side

  =  BC/AB ==> 8/6 ==> 4/3

Example 2 :

From the following diagrams, find the trigonometric ratios of the angle 

Solution :

From the above triangle right angled at C.

AB - hypotenuse side = 25

AC - opposite side = 7 

BC - Adjacent side = 24

sin  θ = Opposite side/Hypotenuse side 

  =  AC/AB ==> 7/25

cos θ = Adjacent side/Hypotenuse side 

  =  BC/AB ==> 24/25

tan θ = Opposite side/Adjacent side 

  =  AC/BC ==> 7/24 

cosec θ = Hypotenuse side/Opposite side

  =  AB/AC ==> 25/7 

sec θ = Hypotenuse side/Adjacent side

  =  AB/BC ==> 25/24

cot θ = Adjacent side/opposite side

  =  BC/AC ==> 24/7

Example 3 :

From the following diagrams, find the trigonometric ratios of the angle 

Solution :

From the above triangle right angled at C.

AB - hypotenuse side = 37

AC - opposite side = 35 

BC - Adjacent side = 12

sin  θ = Opposite side/Hypotenuse side 

  =  AC/AB ==> 35/37

cos θ = Adjacent side/Hypotenuse side 

  =  BC/AB ==> 12/37

tan θ = Opposite side/Adjacent side 

  =  AC/BC ==> 35/12 

cosec θ = Hypotenuse side/Opposite side

  =  AB/AC ==> 37/35 

sec θ = Hypotenuse side/Adjacent side

  =  AB/BC ==> 37/12

cot θ = Adjacent side/opposite side

  =  BC/AC ==> 12/35

After having gone through the stuff given above, we hope that the students would have understood "Find trigonometric ratios using right triangles". 

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