Question

1. technology required. find the perimeter of the figure.

ction to a ratio. you may use

Explanation:

Step1: Draw auxiliary line from A

Draw a line from point \(A\) perpendicular to \(EC\), intersecting \(EC\) at point \(D\). This creates rectangle \(ABCD\), so \(AB = DC = 8\), \(BC = AD = 10\), and \(\angle ADE = 90^\circ\).

Step2: Calculate length of ED

In right triangle \(ADE\), \(\angle AED = 70^\circ\), \(AD = 10\). Use \(\tan(70^\circ)=\frac{AD}{ED}\), so:
\(ED=\frac{AD}{\tan(70^\circ)}=\frac{10}{\tan(70^\circ)}\approx\frac{10}{2.747}\approx3.64\)

Step3: Calculate length of AE

In right triangle \(ADE\), use \(\cos(70^\circ)=\frac{ED}{AE}\), so:
\(AE=\frac{ED}{\cos(70^\circ)}\approx\frac{3.64}{0.342}\approx10.64\)

Step4: Calculate length of EC

\(EC = ED + DC = 3.64 + 8 = 11.64\)

Step5: Sum all sides for perimeter

Perimeter \(P = AB + BC + EC + AE\)

Answer:

\(P\approx8 + 10 + 11.64 + 10.64 = 40.28\)