Question

In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"TSQ")/("tan"∠"PRQ")`

Answer 1

As PS is the median on QR from P.
∴ QS = SR
⇒ QR = 2QS
and RT divides PQ in the ratio 1 : 2
∴ QT = x and PT = 2x
⇒  PQ = 3x

`("tan" ∠"TSQ")/("tan"∠"PRQ")`

= `("QT"/"QS")/("PQ"/"QR")`

= `"QT"/"QS" xx "QR"/"PQ"`

= `x/"QS" xx (2"QS")/(3x)`

= `(2)/(3)`.