Question 1148023
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            The solution by @Boreal is uncompleted.


            The solution by @greenestamps is incorrect.


            I came to bring the correct solution.



<pre>
The right angle is at A, so segments BA and CA are perpendicular. Hence, their slopes are inversely opposite.


AB slope: {{{(5-b)/3}}}

AC slope: {{{b/8}}}


The condition of perpendicularity is <U>THIS equation</U>

    {{{(5-b)/3}}} = {{{-8/b}}}

saying that the slope AC is inversely opposite to the slope AB.


Simplify and solve for "b" :


    {{{5b - b^2}}} = -24

    {{{b^2 - 5b - 24}}} = 0.


Factor the quadratic polynomial in the left side

    (b-8)*(b+3) = 0.


The two roots are  b= 8  and  b= -3.


<U>ANSWER</U>.  The problem has two solutions  b= 8  and  b= -3.
</pre>

Solved and completed.