Plz asap similar and congruent triangles

We know that

in the triangle ROA
tan (∡ROA)=12/5
(∡ROA)=arc tan(12/5)> 67.38°

in the triangle OPA
(∡POA)=(∡ROA)> 67.38°
sin (∡POA)=PA/5> PA=5*sin (67.38°)> 4.62 units

the answer is
PA=4.62 units

alternative method

in the triangle ROA
RO²=12²+5²> RO=13 units
sin (∡ROA)=12/13

in the triangle OPA
(∡POA)=(∡ROA)
sin (∡POA)=12/13
sin (∡POA)=PA/5
12/13=PA/5> PA=12*5/13> PA=4.62 units

The answer is the numbers between =5 and 5