Q. 104.5( 286 Votes )

# In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P.

Answer :

Given that, PR + QR = 25

PQ = 5

Let PR be *x*

Therefore,

QR = 25 - *x*

Pythagoras Theorem: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Applying Pythagoras theorem in ΔPQR, we obtain

PR^{2} = PQ^{2} + QR^{2}

*x*^{2} = (5)^{2} + (25 - *x*)^{2}

*x*^{2} = 25 + 625 + *x*^{2} - 50*x [as, (a + b) ^{2} = a^{2} + b^{2} + 2ab]*

50*x* = 650

*x* = 13

Therefore,

PR = 13 cm

QR = (25 - 13) cm = 12 cm

and we know,sin P =

cos P =

tan P =

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