Question

(b) In APQR, ZQ = 90°. If PQ = 40 cm and PR + QR = 50 cm, find :
(ii) cos P
(iii) tan R.
(i) sin P​

Answer 1

Answer:

cosP = PQ/PR = 40/41

tanR = PQ/QR = 40/9

sinP = QR/PR = /9/41

Step-by-step explanation:

Δ PQR ⇒ angle Q = 90

Use pythagoras theorem

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

∴$PR^{2} - QR^{2} = 40^{2}$

∴ (PR + QR) - (PR-QR) = 1600

∴ 50 * (PR-QR) = 1600

∴ PR- QR = 32

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Now add PR + QR = 50 & PR- QR = 32 and solve equation

we get PR = 41 & QR = 9

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Now,

cosP = PQ/PR = 40/41

tanR = PQ/QR = 40/9

sinP = QR/PR = /9/41