The length of the shadow of a building is 100 meters, as shown below:
The shadow of a building is 100 meters long. The acute angle that the shadow makes with the line joining the tip of the building to the end of the shadow measures 45 degrees.
What is the height of the building?
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OpenStudy (anonymous):
OpenStudy (anonymous):
@dan815 @jim_thompson5910 @zzr0ck3r @HS_CA
jimthompson5910 (jim_thompson5910):
how far did you get?
OpenStudy (anonymous):
not far
jimthompson5910 (jim_thompson5910):
do you have an equation set up?
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OpenStudy (anonymous):
thats my problem
jimthompson5910 (jim_thompson5910):
|dw:1441154654870:dw|
jimthompson5910 (jim_thompson5910):
with respect to the 45 degree angle, we can add these labels
|dw:1441154698897:dw|
jimthompson5910 (jim_thompson5910):
which trig function will we use?
OpenStudy (anonymous):
tangent
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jimthompson5910 (jim_thompson5910):
yes since tan(angle) = opp/adj
jimthompson5910 (jim_thompson5910):
so tan(45) = h/100
jimthompson5910 (jim_thompson5910):
are you able to isolate h in `tan(45) = h/100` ?
OpenStudy (anonymous):
no clue
jimthompson5910 (jim_thompson5910):
it might help to evaluate tan(45) first
use this calculator
http://web2.0calc.com/
to find the value of `tan(45)` and tell me what that is
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OpenStudy (anonymous):
1
jimthompson5910 (jim_thompson5910):
yep
jimthompson5910 (jim_thompson5910):
so `tan(45) = h/100` is the same as `1 = h/100`
jimthompson5910 (jim_thompson5910):
so h = ??
OpenStudy (anonymous):
100
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jimthompson5910 (jim_thompson5910):
good
jimthompson5910 (jim_thompson5910):
this is a 45-45-90 triangle with congruent legs
OpenStudy (anonymous):
wait is that it? 100 is the answer?
OpenStudy (anonymous):
thanks :D
jimthompson5910 (jim_thompson5910):
yeah you multiply both sides of `1 = h/100` by 100 to isolate h, you'll find that h = 100