SOLUTION: The angles of elevation of an office building as observed from the top and ground level of a 10 meters tall residential building are 68° and 72° respectively. How tall is the build

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Question 980108: The angles of elevation of an office building as observed from the top and ground level of a 10 meters tall residential building are 68° and 72° respectively. How tall is the building? How far apart are the two buildings?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The angles of elevation of an office building as observed from the top and ground level of a 10 meters tall residential building are 68° and 72° respectively.
How tall is the building? How far apart are the two buildings?
:
let h = the height of the building
let d = the distance between the two buildings
:
Draw this out labeling the angles the height, and distance
note there are two right triangles formed both a base = d
We can use the tangents of the angles here (side opposite/side adjacent)
:
tan(72) = h%2Fd (from the bottom of the observation building)
find the tangent and rearrange to
d = h%2F3.07768
and
tan(68) = %28%28h-10%29%29%2Fd (from the top of the observation building)
d = %28%28h-10%29%29%2F2.4751
d=d, therefore
%28%28h-10%29%29%2F2.4751 = h%2F3.07768
Cross multiply
3.07768(h-10) = 2.4751h
3.07768h - 30.7768 = 2.4751h
3.07768h - 2.4751h = 30.7768
.6026h = 30.7768
h = 30.7768/.6026
h = 51.1 meters is the height of the building
then
d =
d = 16.6 meters
:
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Did this make sense to you? ankor@att.net