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Question
In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of sin ∠PQS
Solution
tan R = `(5)/(12)`
⇒ `"PQ"/"QR" = (5)/(12)`
⇒ PQ = 5 and QR = 12
In right-angled ΔPQR,
PR
= PQ2 + QR2
= 52 + 122
= 25 + 144
= 169
⇒ PR = 13
∠PQS + ∠P = 90° and ∠P + ∠R = 90°
⇒ ∠PQS + ∠P = ∠P +∠R
⇒ ∠PQS = ∠R
∴ sin ∠PQS
= sin R
= `"PQ"/"PR"`
= `(5)/(13)`.
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