Question

 In triangle 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 1

■Solutions■

✧In right - angled△PQR

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■ PR² = PQ² + QR² ■

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=> PQ² = PR² - QR²

=> (5)² = (PR + QR) (PR - QR)

=> 25 = 25 (PR - QR)

=> 25/25 = PR - QR

=> PR - QR = 1 _________(i)

Or PR + QR = 25 __________(ii)

✧On adding equation (i) and (ii)

✧We get,

• 2PR = 26

=> PR = 26/2

=> PR = 13cm

✧From equation (i)

• PR - QR = 1

=> QR = 13 - 1

=> QR = 12cm

• sin P = QR/PR = 12/13 ;
• cos P = PQ/PR = 5/13 ;
• tan P = QR/PQ = 12/5 .

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