Question 909066
<pre>
There can be no such triangle. It can be shown that the minimum altitude
from R which a triangle SPR can have with an inscribed circle of 
radius 3 and SP =7 is when such triangle SPR is isosceles.  And that
is when the altitude from R is {{{294/13}}} or {{{22&8/13}}}.  So
no such triangle can have an altitude from R as short as 15, as your
problem states. 

The isosceles triangle SPR below is drawn to scale, with SP = 7,
and the inscribed circle has radius 3. Using similar right 
triangles OBR and PAR, it's easy to show that AR = {{{294/13}}}.
Thus altitude RA cannot possibly be as short as 15, `for this is
the minimum case.  You should point this out to your instructor.
There could have been a typo in one of the numbers.

{{{drawing(128,400,-4,4,-1,24,
locate(0,23.1,R),locate(-3.5,0,S),locate(3.5,0,P),
green(line(0,3,2.964705882,3.458823529),line(0,0,0,294/13)),
locate(0,0,A), locate(-.7,3.5,O),locate(3,4.1,B),
triangle(-3.5,0,0,294/13,3.5,0), circle(0,3,3) )}}} 

Edwin</pre>