A person standing exactly midway between two towers observes the top of the two towers at angle of e...........

Quantitative Aptitude ( CCS) Height and Distance

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° = √2−1)

1−2√2 : 1

1+2√2 : 1

3+2√2 : 1

3−2√2 : 1

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Explanation:

Quantitative Aptitude : Height and Distance
Let ED be the taller tower and AB be the shorter tower.
Let C be the point of observation.
Given that angle ACB = 22.5° and angle DCE = 67.5°
Given that C is the midpoint of BD.
Hence, BC = CD
From the right ABC,
tan22.5°=AB /BC?(eq:1)
From the right CDE,
tan67.5°=ED /CD?(eq:2)