What is the size of angle Q when the triangle PQR has vertices of 5 9 and 14 -3 and 2 3 repectively showing work?

The given vertices works out as a right angle triangle when plotted on the Cartesian plane and using the distance formula its dimensions with respect to Q are:-

Hypotenuse: 15

Adjacent: 6 Times Square root of 5

Opposite: 3 times square root of 5

Using any of the 3 trigonometry ratiOS angle Q works out as in the following:-

sin-1(opp/hyp) = 26.6 degrees to 3 significant figures

tan-1(opp/adj) = 26.6 degrees rounded to 1 decimal place

cos-1(adj/hyp) = 26.6 degrees to the nearest tenth