Question

A man who is 5.5ft tall standing 7ft away from a two story building 45 ft high. What is the angle of elevation to the top of the building?

Answer 1

Angle of elevation of the building as viewed by the man

`hat(alpha-beta) ~~ 80^@`

Explanation:

Given : `AB = h = 5.5’, CD = H = 45’, BD = b = 7’`

To find angle of elevation `hat (alpha - beta)`

`tan (alpha - beta) = (H-h) / b`

`H - h = CD - DE = CD - AB = 45 - 5.5 = 39.5’`

`:. tan (alpha - beta ) =H - h) / b = 39.5 / 7 = 5.6429`

Angle of elevation of the building as viewed by the man

`color(blue)(hat(alpha-beta) = tan^-1 (5.6429) ~~ 80^@`

Angle of elevation of the building from the ground

`alpha =tan ^-1 (( CD) / (BD )) = tan ^-1 (H / b ) = tan ^-1 (45 / 7 ) = H / b = color (red)(81.16^@`