In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P

Dear Student

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,
PR^2= PQ^2+ QR^2
Substitute the value of PR as x
(25- x) ^2= 52+ x^2
25^2+ x^2–50x = 25 + x^2
625 + x^2-50x -25–x^2= 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

Thanks