Question 1148023
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corrected response....  the slopes are negative reciprocals, not equal!<br>
The right angle is at A, so segments BA and CA are perpendicular; so the product of their slopes is -1.<br>
AB slope: (5-b)/3
AC slope: b/8<br>
{{{((5-b)/3) * (b/8) = -1}}}
{{{5b-b^2/24 = -1}}}
{{{b^2-5b = 24}}}
{{{b^2-5b-24 = 0}}}
{{{(b-8)(b+3) = 0}}}
{{{b = 8}}} or {{{b = -3}}}<br>