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Question
In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of tan ∠SQR
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
∠SQR +∠R = 90° and ∠R + ∠P = 90°
⇒ ∠SQR + ∠R =∠R + ∠P
⇒ ∠SQR = ∠P
∴ tan ∠SQR
= tan P
= `"QR"/"PQ"`
= `(12)/(5)`.
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