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Trigonometry - Finding a side

Updated on October 4, 2010

Trigonometry – Finding the side

 

Example 1:-

Find the value of x

Here we are going to be using trigonometry to find the side.

S O/H         C A/H         T O/A

 

 

First we need to identify the two sides we are dealing with in this question.

The “x” is directly opposite the 35 degrees

The 12 is the longest side of the right angled triangle and is known as the hypotenuse.

So you see we are dealing with opposite and hypotenuse

 

Using The Calculator

 

Example 2

Using the trigonometric ratios find   X

 

     S O/H       C A/H      T O/A

 

Here we need to identify the sides we are dealing with;

We see that the 14.5 is the longest side of the right angled triangle so it is the Hypotenuse.

The X is adjacent to the 37o

 

So we are dealing with the hypotenuse  and the adjacent.

Example 3

 

Once again use the trigonometric ratios to find   X

 

S O/H       C A/H      T O/A

Again we need to identify the sides we are dealing with;

 

The “x” is directly opposite the 62o degrees

 

And the 17 is adjacent to the 62o degrees

 

So we are dealing with the opposite and the adjacent.

 

In the above three examples "X" was the numerator ,so we multiplied to get "X" on its own.

 

In these next examples "X" is the denominator , so we will have to multiply and then divide to get "X" on its own.

 

Just as above I will do an example using each Trigonometric Ratio

 

 

Example 1

 

 

Using the trigonometric ratios find   X

 

S O/H       C A/H      T O/A

 

Here we need to identify the sides we are dealing with;

We see that the X is the longest side of the right angled triangle so it is the Hypotenuse.

The 12 is adjacent to the 35o

 

So we are dealing with the hypotenuse and the adjacent.

 

This time X is the denominator so make sure you write your equations down properly!

Example 2

 

Again use the trigonometric ratios to find   X

 

S O/H       C A/H      T O/A

 

Identify the sides we are dealing with;

We see that the X is the longest side of the right angled triangle so it is the Hypotenuse.

The 15 is opposite the 45o

 

So we are dealing with the hypotenuse and the opposite.

 

Again X is the denominator so make sure you write your equations down properly!

Example 3

 

 

Using the trigonometric ratios find   X

 

S O/H       C A/H      T O/A

 

Here we need to identify the sides we are dealing with;

 

We see that the 17 is opposite the 32o

 

The X is adjacent to the 32o

 

So we are dealing with the opposite and the adjacent.

 

This time X is the denominator so make sure you write your equations down properly!

 

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    • t.elia profile image
      Author

      t.elia 4 years ago from Northern Ireland

    • t.elia profile image
      Author

      t.elia 4 years ago from Northern Ireland

      Thankyou :)

    • whitneyxox4 profile image

      whitneyxox4 4 years ago from usa

      great. helped clarify a lot :) thank you.