Question

In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of tan ∠SQR

Answer 1

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)`.