Question 108582
S - Short Leg
L - Long Leg
H - Hypotenuse
{{{S^2+L^2=H^2}}}
{{{H=2.8}}}
{{{L=1.7+S}}}
{{{S^2+L^2=H^2}}}
{{{S^2+(1.7+S)^2=(2.8)^2}}}
{{{S^2+(2.89+3.4S+S^2)=7.84}}}
{{{2S^2+3.4S-4.95=0}}}

{{{S = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{S = (-3.4 +- sqrt(3.4^2-4*(2)*(-4.95) ))/(2*2) }}} 
{{{S = (-3.4 +- sqrt(11.56+39.6))/(4) }}} 
{{{S = (-3.4 +- sqrt(51.16))/(4) }}} 
{{{S = (-3.4 +- 7.153)/(4) }}} 
Only the positive root make sense in this case. 
{{{S = (-3.4 + 7.153)/(4) }}} 
{{{highlight(S = 0.94)}}} 
{{{L=1.7+S}}}
{{{L=1.7+.94}}}
{{{highlight(L=2.64)}}}
Verify your answer. 
{{{S^2+L^2=H^2}}}
{{{0.94^2+2.64^2=2.8^2}}}
{{{0.88+6.97=7.84}}}
{{{7.85=7.84}}} Close enough from roundoff error.
Good answer.
S=0.94 units
L=2.64 units