Question

PLZ HELP ASAP SIMILAR AND CONGRUENT TRIANGLES

Answer 1

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