Question

in triangle PQR right angled at Q, QR = 3cm and PR-PQ= 1cm. determine the values of Sin R, Cos R and tan R.

Answer 1

Given : triangle PQR right angled at Q, QR = 3cm and PR-PQ= 1cm

To Find : values of Sin R, Cos R and tan R.

Solution:

triangle PQR right angled at Q,

Using Pythagoras theorem

=> PR² = PQ² + QR²

=> PR² - PQ² = QR²

using a² -  b² = (a + b)(a - b)

=> (PR + PQ )(PR - PQ) = QR²

PR - PQ = 1 , QR = 3  Given

=> (PR + PQ) (1) = 3²

=> PR + PQ  = 9

    PR - PQ  = 1

Adding both 2PR = 10  => PR = 5

5 + PQ = 9 => PQ = 4

=> PR = 5  , PQ =  4  

PR = 5  , PQ =  4   QR  =  3

Sin R = PQ/PR  = 4/5

Cos R = QR/PR  = 3/5

Tan R  = PQ/QR  =  3  

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Answer 2

Given : triangle PQR right angled at Q, QR = 3cm and PR-PQ= 1cm

To Find : values of Sin R, Cos R and tan R.

Solution:

triangle PQR right angled at Q,

Using Pythagoras theorem

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

=>$PR^2 - PQ^2 = QR^2$

using $a^2 - b^2 = (a + b)(a - b)$

=>$(PR + PQ )(PR - PQ) = QR^2$

PR - PQ = 1 , QR = 3  Given

=> $(PR + PQ) (1) = 3^2$

=>$PR + PQ = 9$

  $PR - PQ = 1$

Adding both 2PR = 10  => PR = 5

$5 + PQ = 9 = > PQ = 4$

$= > PR = 5 , PQ = 4$

$PR = 5 , PQ = 4 QR = 3$

$Sin R = PQ/PR = 4/5$

$Cos R = QR/PR = 3/5$

$Tan R = PQ/QR = 3$

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