Question

If m = 60° and PE = 3, then PB = 3√2 3√3 6

Answer 1

The complete question asks "If  mDB = 60° and PE = 3, then PB =?"

The correct answer is C) PB = 6.

Explanation:
See the attached picture for reference.

We know
∠DBP = 60°

PB ≡ PD because they are both radius of the circunference, which means that ΔPDB is an isosceles triangle of base DB.

As a consequence, ∠DBP ≡ ∠PDB = 60°.

But then ∠DPB = 180 - 60 - 60 = 60°.

An isosceles triangles with all the angles measuring 60° is an equilateral triangle.

In an equilateral triangle, the height (DE) cuts into to equl parts the side PB, which means that PE = (1/2) PB

We know PE = 3, therefore 
PB = 2 × PE
      = 2 × 3
      = 6

Hence, PB = 6.