Question

Find the value of the variable. if your answer is not an integer, leave it in simplest radical form.

Answer 1

\[\frac{x}{5}=\frac{\sqrt{2}}{2}\] so

Answer 2

triangle is equilateral, because both angles must be 45 degrees

Answer 3

\[\sin(45)=\frac{ x }{ 5 }\]
\[x=5\sin(45)=5\frac{ \sqrt{2} }{ 2 }=\frac{ 5\sqrt{2} }{ 2 }\]

Answer 4

so
\[x^2+x^2=25\implies 2x^2=25\implies x\sqrt{2}=5\implies x=\frac{5}{\sqrt{2}}\]

Answer 5

Triangle is actually not "equilateral" . It's isosoles right or 45-45-90. If your recognize that and not the ratio of the sides for 45 45 90s. Given the hyp is 5, you can answer straight away that the legs are each 5 / sqrt(2)