Question

A person standing d=145 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is a=14 degrees, while the angle of elevation to the top of the mirror is b=11 degrees. Find the vertical dimension of the mirror

Answer 1

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:

$tan(11) = \frac{AB}{BO}\\ \\0.195 = \frac{AB}{145} \\\\AB = 28.275 cm$

For the angle of depression:

$tan(14) = \frac{BC}{BO} \\\\0.25 = \frac{BC}{145} \\\\BC = 36.25 cm$

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