Final answer:
To solve for PK in triangle KPS, calculate the third angle K using the angle sum property and then apply the Law of Sines with the given side PS and angles P and S.
Step-by-step explanation:
The question involves solving for the length of side PK in triangle KPS, using the given angles and side length. We are told that m∠P is 105°, m∠S is 30°, and PS is 12 units. Knowing two angles allows us to calculate the third angle in the triangle using the fact that the sum of angles in a triangle is 180°. Once the third angle is known, we can use the Law of Sines to find PK.
First, find the measure of ∠K:
180° - 105° - 30° = 45°.
Now use the Law of Sines:
PK/sin(105°) = 12/sin(45°)
PK = 12 × sin(105°) / sin(45°)
Calculate the value using a calculator to find PK.