Question

In △ABC, ∠ABC = 60 degrees .

Answer 1

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 $180^{o}$.

In the given question, point P is center of the given triangle such that <APB = <APC = <BPC = $120^{o}$. Such that line PB bisects <ABC into two equal measures of $30^{o}$.

Thus;

<ABP = $30^{o}$

Thus,

<ABP + <APB + <BAP = $180^{o}$

30 + 120 + <BAP = $180^{o}$

<BAP = $180^{o}$ - 150

<BAP = $30^{o}$

Apply the Sine rule to determine the value of PB, such that;

$\frac{a}{SinA}$ = $\frac{b}{SinB}$

$\frac{8}{Sin 30}$ = $\frac{PB}{Sin 30}$

BP = $\frac{8*Sin 30}{Sin 30}$

    = 8

BP = 8.0

Therefore, the value of PB = 8 units.

For more clarifications on Sine rule, visit: brainly.com/question/27174058

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