How to find coordinates on terminal arm

Question

The angle theta is in the first quadrant and sin of theta = 2/sqrt(13)

determine the possible coordinates for point P on the terminal arm

Answer 1

sin=opposite/hypotenuse

sin=2/√13

draw a right triangle in quadrant I

you know the hypotenuse and the opposite side but not the adjacent side

use the Pythagorean Theorem

(√13)²=2²+a² where a=adjacent side

13=4+a²

a²=13-4

a²=9

a=√9

a=3

point: P=(3,2) for the value of sin that is given, which is one of infinitely many points if the sides of the triangle are all extended (doubled, tripled,...), or shortened (1/2 each side, 1/4 each side,...)

other points are P=(6,4), P=(9,6), ...