Problem #2:
Given 45-45-90 triangle
The triangle is an isosceles right triangle
so, the legs are congruent ⇒ a = b
Using the Pythagorean theorem
[tex]a^2+b^2=(\text{hypotenuse)}^2[/tex]
as shown, hypotenuse = 7√2
so,
[tex]\begin{gathered} a^2+b^2=(7\sqrt[]{2})^2 \\ a^2+b^2=98\rightarrow(a=b) \\ a^2+a^2=98 \\ 2a^2=98 \\ a^2=\frac{98}{2}=49 \\ a=\sqrt[]{49}=7 \end{gathered}[/tex]
so, the answer will be:
[tex]\begin{gathered} a=7 \\ b=7 \end{gathered}[/tex]
Another method:
The length of the side opposite to the angle 45 = hypotenuse/√2
So,
[tex]a=b=\frac{7\sqrt[]{2}}{\sqrt[]{2}}=7\operatorname{cm}[/tex]
