1.

In triangle POR, right angle at Q, PR + QR = 25cm and PQ = 5cm. Determine the value of sin P, cos P and tanP. @shreeya21

Answer»

Given :

<P>
  • PQR is a RIGHT angled triangle .
  • angle Q = 90°
  • PQ = 5 cm
  • PR + QR = 25 cm

To find :

  • Sin P
  • Cos P
  • Tan P

Solution:

USING PGT in triangle PQR

PR² = PQ² + QR² _____(1)

PR² = 5² + QR²

PR² - QR² = 25

(PR + QR) (PR - QR) = 25

25 (PR - QR) = 25

PR - QR = 25/25

PR - QR = 1

PR = 1 + QR

Using this in equation (1)

PR² = PQ² + QR²

(1+QR)² = 5² + QR²

1 + QR² + 2QR = 25 + QR²

1 + 2QR = 25

2QR = 25 -1

2QR = 24

QR = 24/2

QR = 12 cm

PR = 1 + QR

PR = 1+12 = 13 cm

From the figure ,

\implies Sin P = \tt \dfrac{Perpendicular}{Hypotenuse}

= QR/PR

= 12/13

\implies Cos P = \tt \dfrac{Base}{Hypotenuse}

= PQ/PR

= 5/13

\implies Tan P =\tt \dfrac{Perpendicular}{Base}

= QR/PQ

= 12/5


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