(A) In a right angled triangle PQR, an altitude RS is drawn from the vertex R of the right angle. The respective perpendicular distances of the point S from the sides PR and QR are 6 and 3.

Determine the length of PR.

(B) What would have been the length of PR if the respective perpendicular distances of the point S from the sides PR and QR were 8 and 4?

Let angle SRB = a, then tan(a)=BS/BR=1/2
By alternate angles property,taking BR and AS as parallel lines
and RS is the line that cuts both of them,
angle ASR= angle BRS = a
So, angle ASP = 90 - angle ASR= 90-a
which implies that AP = tan(90-a)*AS=cota*AS=2*6=12
PR=AP+AR=12+3=15

Similarly, in second case AP=2*AS+AR=2*8+4=20

Posted by Praneeth Yalavarthi on 2007-07-09 12:03:02