In a given triangle PQR, right angled at Q, the following measures are

PQ = 5 cm

PR + QR = 25 cm

Now let us assume, QR = x

PR = 25 - QR

PR = 25- x

According to the Pythagorean Theorem,

PR² = PQ² + QR²

Substitute the value of PR as x

(25- x) ² = 5² + x²

25² + x² – 50x = 25 + x²

625 + x²-50x -25 – x² = 0

-50x = -600

x= -600/-50

x = 12 = QR

Now, find the value of PR

PR = 25 - QR

Substitute the value of QR

PR = 25 - 12

PR = 13

Now, substitute the value to the given problem

(1) sin p = Opposite Side/Hypotenuse = QR/PR = 12/13

(2) Cos p = Adjacent Side/Hypotenuse = PQ/PR = 5/13

(3) tan p =Opposite Side/Adjacent side = QR/PQ = 12/5