In every 45-45-90 triangle, both legs have the same length and the hypotenuse has the length of a leg multiplied by √2.
The hypotenuse is the side opposite to the right angle (90º). The other two sides are the legs that have the same length.
In the question b., the hypotenuse has a length b and the missing leg has a length a.
Since the leg of the triangle has a measure of 2.5ft, then the leg a must have the same measure. Then:
[tex]a=2.5ft[/tex]
The hypotenuse has the length of a leg multiplied by √2. Then:
[tex]\begin{gathered} b=2.5\times\sqrt[]{2}ft \\ =\frac{2\times2.5\times\sqrt[]{2}}{2}ft \\ =\frac{5\cdot\sqrt[]{2}}{2}ft \\ \approx3.5355\ldots ft \end{gathered}[/tex]
Therefore, the lengths of a and b in the question b., are:
[tex]\begin{gathered} a=2.5ft \\ b=\frac{5\cdot\sqrt[]{2}}{2}ft\approx3.5ft \end{gathered}[/tex]
