HOW TO FIND THE MISSING SIDE OF A TRIANGLE USING TRIGONOMETRY

How to Find the Missing Side of a Triangle Using Trigonometry :

Here we are going to see how to find the missing sides of the triangle.

In this section we are going to have some right triangles, in which we have some missing sides.To find the measure of missing side of the right triangle we use the following 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 look into some example problems to understand how to find the missing side of the triangle using trigonometric ratios.

Example 1 :

Find the measure of each side indicated. Round to the nearest tenth. Solution :

Hypotenuse side  =  AB

Opposite side  =  BC   =  4

Adjacent side  =  AC  =  x

Here θ is 41°

The sides opposite and adjacent are involving in the trigonometric ratio tan θ

tan θ  =  Opposite side/Adjacent side  =  BC/AC

tan 41°  =  4/x

0.86  =  4/x

x =  4/0.86

=  4.65

Hence the measure of missing side is 4.6.

Example 2 :

Find the measure of each side indicated. Round to the nearest tenth. Solution :

Hypotenuse side  =  AB  =  x

Opposite side  =  AC   =  10.8

Adjacent side  =  BC

Here θ is 57°

The sides opposite and hypotenuse are involving in the trigonometric ratio sin θ

sin θ  =  Opposite side/Hypotenuse side  =  AC/AB

sin 57°  =  10.8/x

0.83  =  10.8/x

x =  10.8/0.83

=  13.01

Hence the measure of missing side is 13

Example 3 :

Find the measure of each side indicated. Round to the nearest tenth. Solution :

Hypotenuse side  =  AB  =  10.3

Opposite side  =  AC   =  x

Adjacent side  =  BC

Here θ is 37°

The sides opposite and hypotenuse are involving in the trigonometric ratio sin θ

sin θ  =  Opposite side/Hypotenuse side  =  AC/AB

sin 37°  =  x/10.3

0.60  =  x/10.3

x =  10.3(0.60)

=  6.18

Hence the measure of missing side is 6.1 After having gone through the stuff given above, we hope that the students would have understood how to find missing side of a triangle using the concepts in trigonometry.

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