Mammoth Memory

Examples using sine rule

You can use the sine rule (If you can remember it – but why try) here it is anyway:

Example 1

Find the length of `x` in the following diagram?

Example 1  find the length of X in the diagram

Solution:

The sine rule: `a/sinA=b/sinB=c/sinC` 

In a triangle that looks like:

Sine and Cosine are used to find the angle of a shape

Therefore use:

`a/sinA` `=` `b/sinB`
`a/sin80` `=` `7/sin60`
`a` `=` `(7timessin80)/sin60`
`a` `=` `6.893/0.866`
`a` `=` `7.959`

 

Answer: `x=7.959`

 

Example 2

Find angle A

Example 2 find angle A

Solution:

The sine rule: `a/sinA=b/sinB=c/sinC`

In a triangle that looks like:

Sine and Cosine are used to find the angle of a shape

Therefore Use:

`a/sinA` `=` `c/sinC`
`4.8/sinA` `=` `5.7/sin63`
`(4.8timessin63)/5.7` `=` `sinA`

 Or

`sinA` `=` `(4.8timessin63)/5.7`
`sinA` `=` `4.276/5.7`
`sinA` `=` `0.75`

 

Answer: `A=48.61^@`

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