SOLUTION: 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 angl

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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?
Answer by mananth(16946) (Show Source):
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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