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: $A=48.61^@$