Question

geometrysolve for x and y: geometric meanset proportions and then solveplease help, i'm strugglingstep by step answers+ explanations would be greatly appreciated

Answer 1

Because we have similar triangles we can assume the angle in green (angle theta) is equal

Using a trigonometric expression we can assume the next equality

`(x)/(8)=(3)/(x)`

We need to clear x

`\begin{gathered} x^2=3(8) \\ x^2=24 \\ x=\sqrt[]{24}=2\sqrt[]{6} \end{gathered}`

then we can calculate y using the Pythagorean theorem

`\begin{gathered} y^2=x^2+3^2=24+9=33 \\ y=\sqrt[]{33} \end{gathered}`