First off, we know a decagon has 10 sides. Secondly, it is given that the total side length is 8 feet- split in half it's 4 and 4 (this will come into play in the formula). Next, we want to find the angle measure of one of the isosceles triangles. Thus, do 360/10 which gives 36. Then do 36/2 which equals 18. This is the angle measure we need. Now that we have the necessary information, we can set up the formula. Following SOHCAHTOA, we can see that we need to use the tangent to find the apothem since our opposite side length of 4 is given. Set up the equation like so: tan18 = 4/a. When plugged in and solved, the answer of 12.31073415 is received.
