Answer:
PA ≈ 4.62 units
Step-by-step explanation:
∠ AOP = ∠ ORB ( alternate angles )
∠ APO = ∠ RBO ( both right angles ), thus
Δ ORB and Δ AOP are similar by the AA postulate.
Thus the ratios of corresponding sides are equal, that is
[tex]\frac{OR}{AO}[/tex] = [tex]\frac{BO}{PA}[/tex], substitute values
In right triangle RBO, BO = 13 (5- 12- 13 right triangle )
[tex]\frac{13}{5}[/tex] = [tex]\frac{12}{PA}[/tex] ( cross- multiply )
13PA = 60 ( divide both sides by 13 )
PA ≈ 4.62 ( to the nearest hundredth )
