Question

PLEASE ANSWER ASAP
IGiven: △KPS m∠P=105°, m∠S=30° PS = 12 Find: PK

Answer 1

$PK= 8.5$

Step-by-step explanation:

=> The sum of interior angles of a triangle is 180°.

$m < k \: + \: m < p \: + \: m \: < s = 180°$

$m < k \: + \: 30 = 180°$

$m < k \: + 135 = 180°$

=> Subtract 135° from both sides

$m < k = 45°$

=> Now use sine rule

$\frac{sinA}{a} + \frac{sinB}{b}$

$\frac{sinK}{PS} + \frac{sinS}{PK}$

$\frac{sin(45)}{12} + \frac{sin(30)}{PK}$

=> Cross multiply

$PKsin(45) = 12sin(30)$

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

$PK= 8.5$

Hope it helps :)