STEP 1: find side $ x $

To find side $ x $ use Pythagorean Theorem:

$$ h^2 + x^2 = c^2 $$

After substituting $h = 5\, \text{in}$ and $c = 6\, \text{in}$ we have:

$$ \left( 5\, \text{in} \right)^{2} + x^2 = \left( 6\, \text{in} \right)^{2} $$ $$ x^2 = \left( 6\, \text{in} \right)^{2} - \left( 5\, \text{in} \right)^{2} $$ $$ x^2 = 36\, \text{in}^2 - 25\, \text{in}^2 $$ $$ x^2 = 11\, \text{in}^2 $$ $$ x = \sqrt{ 11\, \text{in}^2 } $$$$ x = \sqrt{ 11 }\, \text{in} $$

STEP 2: find short base $ b $

To find short base $ b $ use formula:

$$ x = \frac{ a - b } { 2 } $$

After substituting $x = \sqrt{ 11 }\, \text{in}$ and $a = 15\, \text{in}$ we have:

$$ \sqrt{ 11 }\, \text{in} = \frac{ 15\, \text{in} - b } { 2 } $$ $$ \sqrt{ 11 }\, \text{in} \cdot 2 = 15\, \text{in} - b $$ $$ 15\, \text{in} - b = 2 \sqrt{ 11 }\, \text{in} $$ $$ b = 15\, \text{in} - 2 \sqrt{ 11 }\, \text{in} $$ $$ b = 8.3668\, \text{in} $$

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