Question

in triangle PQR, right angled at q ,PR+QR=25CM and PQ=5CM. Determine the values of sin P, cos P and tan P.

Answer 1

Given PR + QR = 25 , PQ = 5
PR be x.  and QR = 25 - x 

Pythagoras theorem ,PR2 = PQ2 + QR2

x2 = (5)2 + (25 - x)2

x2 = 25 + 625 + x2 - 50x
50x = 650
x = 13
 

 PR = 13 cm
QR = (25 - 13) cm = 12 cm

sin P = QR/PR = 12/13

cos P = PQ/PR = 5/13

tan P = QR/PQ = 12/5 

Answer 2

Answer:

Sin P=12/13  , tan P=12/5

Step-by-step explanation:

Let PR be 'x' and QR be = 25-x

Using Pythagorus Theorem,

==>PR^2 = PQ^2 + QR^2

     x^2   = (5)^2 + (25-x)^2

     x^2   = 25 + 625 + x^2 - 50x

     50x   = 650

          x   = 13

therefore, PR = 13 cm

and,          QR = (25 - 13) = 12 cm

Now,  Sin P = opposite/hypotenuse = QR/PR = 12/13

          Tan P= opposite/adjacent      = QR/PQ = 12/5

          Cos P= adjacent/hypotenuse = PQ/PR = 5/13