Triangle FOR is similar to the triangle FAN.
Since Triangle FOR is an isosceles triangle, sides FO and FR will be equal in length i.e. 7.0
Two sides of triangle FOR are FR and OR. The corresponding sides of Triangle FAN are FN and AN. The ratio of corresponding sides of similar triangles is the same, so we can write:
FR : OR = FN : AN
7 : 10 = 10 : AN
⇒
7 x AN = 100
Thus AN = 100/7
Rounded of to nearest hundredth, the answer is 14.29