Question

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

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
∠PQS + ∠P = 90°  and ∠P + ∠R = 90°
⇒ ∠PQS + ∠P = ∠P +∠R
⇒ ∠PQS = ∠R
∴ sin ∠PQS
= sin R

= `"PQ"/"PR"`

= `(5)/(13)`.