Question

8. In a right triangle PQR, right angled at Q, PR - PQ = 1cm and QR = 5cm. Find the value of sin R, cos R and tan R.​

Answer 1

Answer:

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 RPQ/QR = 3

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