Question

$$\begin{array}{cc}& \text{In}△ABC,\angle ABC=\\ & {90}^{\circ },\angle BAC=\angle BCA={45}^{\circ }\text{. If}\end{array}$$
$AC=2\sqrt{2}$, then find the value of $AB$.

Answer 1

$\angle ABC={90}^{\circ }$
$\begin{array}{cc}& \angle BAC=\angle ACB={45}^{\circ }\\ & AC=2\sqrt{2}\end{array}$
To find,
The length of $AB$
Solution,
The length of $AB$ in $△ABC$ is 2 units.
We can simply find the length of $AB$ in $△ABC$ using
Pythagoras Theorem.
In $△ABC$
$\angle BAC=\angle ACB$ (given)
$BC=AB$ (sides opposite to equal angles are equal)
Using Pythagoras theorem in $△ABC$
$\begin{array}{cc}(AC{)}^2& =(AB{)}^2+(BC{)}^2\\ (2\sqrt{2}{)}^2& =(AB{)}^2+(AB{)}^2(AB=BC)\\ 8& =2(AB{)}^2\\ 4& =(AB{)}^2\\ 2& =AB\end{array}$
Hence, the length of the side $AB$ in $△ABC$ is 2 units.