Question

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

Answer 1

Answer:

 PK=8.49m

Explanation:

We have sine formula

     $\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

By sine formula we have

    $\frac{PS}{sinK} =\frac{PK}{sinS} =\frac{KS}{sinP}$

    We have PS = 12, ∠P=105° and ∠S=30°, so ∠K=180°-(105°+30°)=45°

 Substituting

        $\frac{12}{sin45} =\frac{PK}{sin30} \\ \\ PK=8.49m$