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# Trigonometry - Finding a side

## 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 37 ^{o}**

**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 62 ^{o }**

**degrees**

**And the 17 is adjacent to the 62 ^{o }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 35 ^{o}**

^{}

**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 45 ^{o}**

**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 32 ^{o}**

**The X is adjacent to the 32 ^{o}**

**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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