Please explain and show work You are making a circular cutti

Please explain and show work

You are making a circular cutting board. To begin, you glue ten 3-inch boards togethe as shown. Then you draw and cut a circle with a 30-inch diameter from the boards. AD is the diameter of the circle. Write a proportion relating EG to GD. State a theorem to justify your answer. Find AG, GD, and GE. What is the length of the cutting board seam labeled EC? A. B.

Solution

AG+GD = 30 Inch
Triangle EGD is a right angle triangle.

Evne Trianglee AED is also right anle triangle.

let andle GAE is x.

angle AED is 90 degree.

Let angle GED is Y.

Then Angle AEG is 90-y.

GAE+AGE+AEG=180

X+90+90-Y=180

From there we can find X=Y.

Means GAE = GED.

Tan x = EG/GA EQUATION 1

Tanx=GD/EG eq-2

EG/GA = GD/EG

Square of EG = GD*GA

Square of EG = GD(30-GD)

Square of (EG/GD)+1=30/GD.

Sin X = ED/30

Sin X = EG/30-GD

Sin X = GD/ED

ED/30=GD/ED

Square of ED = 30GD.