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In this example, we're asked to use similar triangles
to continue an application problem that was mentioned earlier.
So Mary decides to use what she knows about the height of
the roof, this was of her house, to measure the height of
her second daughter. So Mary had two daughters and she
initially measured the height of her house using
her first daughter, her second daughter now is standing next to the house
13.5 feet away, and she casts a shadow
that's 1.5 feet tall. Mary knows the house
is 25 feet tall. So this piece is information that
we have from a previous example. So the question is how can we use similar
triangles
to help determine the height I've Mary's
daughters. Well let's set up a proportion
with the height of the daughter over the length of her shadow,
and thats going to equal, so thats
this length over this length, is proportional to
this length which is 25 over
this length, so if I add those together
I get 15 feet. So here's the proportion I can use to solve the problem
if I do a cross product here
I get 25 times 1.5
divided by 15
and if I perform that multiplication
25 times 1.5 divided by 15
I get 2.5 and this is in
feet of course so I can say that
Mary's daughter is
2.5 feet tall.
So I imagine that she's fairly young.