3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals...
3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals as shown. Let the diagonals have length. The measure of each interior angle of a regular pentagon is 108° The isosceles triangles ABF and ECD are similar and each have angles 369-36° -1080 (a) Use a proportion for similar triangles ABF and ECD and the quadratic formula, -btVb2-4ac dc to show that x = * (the golden ratio). 2a * 360 x (diagonal) (b) Notice that cos 36° '+v Use the Pythagorean Theorem or a Pythagorean trig identity to determine that sin 360 (c) Use the formula for cos(a - b) to find the exact value of cos 6" You do not have to simplify your answer.