Answer:
x = 5.2
Step-by-step explanation:
Measure of interior angle of a regular polygon = [tex]\frac{(n-2)\times180}{n}[/tex]
Here n = number of sides of the polygon
Interior angle of a regular pentagon = [tex]\frac{(5-2)\times180}{5}[/tex]
= 108°
By applying cosine rule in ΔABK,
(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°
(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°
x² + 6x + 9 = 16 + 36 - (-14.83)
x² + 6x = 57.83
x² + 6x - 57.83 = 0
x = [tex]\frac{-6\pm \sqrt{6^2-4(1)(-57.83)}}{2(1)}[/tex]
x = [tex]\frac{-6\pm16.35}{2}[/tex]
x ≈ -11.2, 5.2
Since, x can't be negative,
x = 5.2 will be the answer.
