The length of the mirror is 64.52 cm
Explanation:
Given:
Distance of the person from the mirror = 145cm
Angle of depression = 14°
Angle of elevation = 11°
Vertical dimension of the mirror = ?
For angle of elevation:
[tex]tan(11) = \frac{AB}{BO}\\ \\0.195 = \frac{AB}{145} \\\\AB = 28.275 cm[/tex]
For the angle of depression:
[tex]tan(14) = \frac{BC}{BO} \\\\0.25 = \frac{BC}{145} \\\\BC = 36.25 cm[/tex]
Total length of the mirror, AC = AB + BC
= 28.275 + 36.25cm
= 64.52 cm
Therefore, the length of the mirror is 64.52 cm
