Question

In terms of trigonometry ratios for triangle BCE what is the length of line CE. Insert text on the triangle to show the length of line CE.When you are done using the formula for the triangle area Area equals 1/2 times base times height write an expression for the area of triangle ABC Base your answer on the work you did above

Answer 1

CE can be written as:

`(BE)/(CE)=(CE)/(AE)`

Solve for CE:

`\begin{gathered} CE^2=BE\cdot AE \\ CE=\sqrt[]{BE\cdot AE} \end{gathered}`

The area is:

`\begin{gathered} A=(b\cdot h)/(2) \\ _{\text{ }}where\colon \\ _{\text{ }}b=AB \\ h=CE=\sqrt[]{BE\cdot AE} \\ so\colon \\ A=\frac{AB\cdot\sqrt[]{BE\cdot AE}}{2} \end{gathered}`