Question

In triangle KPS, if m∠P = 105°, m∠S = 30°, and PS = 12, find the length of PK?

Answer 1

To find the length of PK in triangle KPS, use the Law of Sines and solve for PK.

Step-by-step explanation:

In triangle KPS, the sum of the angles must equal to 180 degrees. We are given that m∠P = 105° and m∠S = 30°. So, m∠K = 180° - (105° + 30°) = 45°.

Now, we can use the Law of Sines to find the length of PK:

sin(105°) / PK = sin(45°) / 12

PK = (sin(45°) / sin(105°)) * 12

Using a calculator, PK ≈ 10.23