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?
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let h = the height of the building
let d = the distance between the two buildings
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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/d}}} (from the bottom of the observation building)
find the tangent and rearrange to
d = {{{h/3.07768}}}
and
tan(68) = {{{((h-10))/d}}} (from the top of the observation building)
d = {{{((h-10))/2.4751}}}
d=d, therefore
{{{((h-10))/2.4751}}} = {{{h/3.07768}}}
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 = {{{51.1/3.07768}}
d = 16.6 meters between the buildings
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Check that, find d using the other equation
d = {{{((51.1-10))/2.4751}}}
d = 16.6 meters
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Did this make sense to you? ankor@att.net