Question

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

Answer 1

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

Answer 2

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