Respuesta :
Answer:
∠PBC = 30°
Step-by-step explanation:
Given that <ABC = 60° and P is equidistance from AB, AC, BC
If P is equidistance from all the side then triangle ABC is equilateral
<ABC = <ACB = <CAB =60 and P is the center of the triangle (characteristics of an equilateral triangle)
If a perpendicular line is drawn from any of the angle through P to any of the opposite side it will divide the side into equal length
For instance AB = AC = BC = 2CM
If we draw a perpendicular line from <ABC through P to AC at point D
Then we will have a right angle triangle BCD : < BDC =90, BC = 2CM, CD =1CM
We can use sine rule to determine the angle
Sine BDC = sine CBD
BC CD
Sine 90 = sine CBD
2 1
1 = sine CBD
2 1
sin CBD = 0.5
<CBD = 30°
<CBD = <PBC = 30°
