A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5° = $$\sqrt 2- 1$$ )

• A. $1 - 2\sqrt 2 :1$$
• B. $1 + 2\sqrt 2 :1$$
• C. $3 + 2\sqrt 2 :1$$
• D. $3 - 2\sqrt 2 :1$$