A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Thus the value of PB is 8.0 units.
A given shape that is bounded by three sides and has got three internal angles is referred to as a triangle. Types of triangles include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The sum of the internal angles of any triangle is [tex]180^{o}[/tex].
In the given question, point P is such that <APB = <APC = <BPC = [tex]120^{o}[/tex]. Also, line PB bisects <ABC into two equal measures. Thus;
<ABP = [tex]30^{o}[/tex]
Thus,
<ABP + <APB + <BAP = [tex]180^{o}[/tex]
30 + 120 + <BAP = [tex]180^{o}[/tex]
<BAP = [tex]180^{o}[/tex] - 150
<BAP = [tex]30^{o}[/tex]
Apply the Sine rule to determine the value of PB, such that;
[tex]\frac{AP}{Sin B}[/tex] = [tex]\frac{BP}{Sin30}[/tex]
[tex]\frac{8}{Sin30}[/tex] = [tex]\frac{BP}{Sin 30}[/tex]
BP = [tex]\frac{8*Sin30}{Sin 30}[/tex]
= [tex]\frac{4}{0.5}[/tex]
BP = 8.0
Therefore, the value of BP = 8 units.
For more clarifications on applications of the Sine rule, visit: https://brainly.com/question/15018190
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