Answer:
2.55
Step-by-step explanation:
Draw a picture of the triangle formed by points P, A, and B. The angle of the line from P to A is 225°. The angle of the line from P to B is 116°. The angle of the line from B to A is 258°, and the length of the line is 3.91.
The easiest way to solve this is by first finding the angle of the line from B to P. Using interior angles, we can show that this is 180° − 116° = 64°.
Next, we can show that:
∠APB = 225° − 116° = 109°
∠ABP = 360° − (258° + 64°) = 38°
Finally, we can use law of sines to find AP.
AP / sin 38° = 3.91 / sin 109°
AP = 2.55
