Question 872221
You are in the smaller building looking out of a window. You sight the top of the taller building at an angle of40 degrees. You sight the bottom of the taller building with an angle of depression of 20 degrees. If the building is 200 feet tall, how high up are you in the smaller building? How far apart are the two buildings?

angle of elevation to the top of taller building = 40 degrees

angle of depression to the bottom of taller building = 20 degrees


Let us assume you are at height h in the smaller building
height of taller building = 200 ft

let the distance between the two buildings be d

tan 20 = h/d


tan 40 = (200-h)/d

tan 20 + tan 40 = h/d + (200-h)/d

tan 20 + tan 40 = 200/d

d= 200/( tan 40 +tan 20 )
d=166.07 feet




Now tan 20 = h/166.07
h = 166.07*tan 20

h = 60.44 feet

you are standing 60.44 feet