The length of PK from the given diagram is 6√2
In order to get the length of PK, we will use the sine rule formula expressed as:
[tex]\frac{PK}{sinm<S} =\frac{PS}{sinm<K}[/tex]
Get the measure of m<K
m<K = 180 - (105+30)
m<K = 180 - 135
m<K = 45degrees
Given
PS = 12
m<S = 30 degrees
Substitute the given parameters into the formula to get PK
[tex]\frac{PK}{sin30} =\frac{12}{sin45}\\\frac{PK}{0.5} = \frac{12}{1/\sqrt{2} }\\\frac{PK}{0.5}=12\sqrt{2} \\PK = \frac{1}{2} \times 12\sqrt{2} \\PK = 6\sqrt{2}[/tex]
Hence the length of PK from the given diagram is 6√2
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