Expert: Josh - 8/1/2008

Question
PQR is a right angled TRAINGLE. Q is right angled.
Now we have PQ+QR = 25 cm here.

So,question is to find the length of each side including hypotenuse.Find PQ ,QR,PR
Also, main thing is to find the SINE and COSINE values here.

SIN(P)=QR/PR  

Answer
Rohit

We can find an expression for each of the things you mentioned, but we do not have all the information required to write the answer(s) as a number.

P
|
|
Q--------R

Let "x" represent the length of |QR|. Since |PQ|+|QR|=25, |PQ|=25-x.

Using Pythagoras theorem, the hypotenuse is given by sqrt(|PQ|^2+|QR|^2) = sqrt(x^2+(25-x)^2) = sqrt(2x^2-50x+625). For convenience, let H=sqrt(2x^2-50x+625). This, of course, is same as |PR|.

Using standard definitions:
sin(P)=|QR|/|PR|=x/H          (opposite side/hypotenuse)
cos(P)=|PQ|/|PR|=(25-x)/H     (adjacent side/hypotenuse)

Unless we know the angle P, we cannot go further. The main thing is that H also depends on the dimension x.