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sattari [20]
4 years ago
8

Given: △KPS m∠P=105°, m∠S=30° PS=12 Find: PK.

Mathematics
2 answers:
leonid [27]4 years ago
7 0

split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2

vfiekz [6]4 years ago
6 0

Answer:

PK= 8.5

Step-by-step explanation:

The sum of interior angles in a triangle is 180 degree

m

m

m

Subtract 135 from both sides

m

Now use sine rule

\frac{sin A}{a} =\frac{sin B}{b}

\frac{sin K}{PS} =\frac{sin S}{PK}

\frac{sin(45)}{12} =\frac{sin(30)}{PK}

Cross multiply

PKsin(45)}=12sin(30)

PK =\frac{12sin(30)}{sin(45)}

PK= 8.5

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