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We basically have this triangle set up:
To find the unknown length, we need to use the Pythagorean Theorem.
Remember, the Pythagorean Theorem is
where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.
Since the legs are
and
this means that
and
Also, since the hypotenuse is
, this means that
.
Start with the Pythagorean theorem.
Plug in
,
,
Square
to get
.
Square
to get
.
Subtract
from both sides.
Combine like terms.
Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).
Simplify the square root.
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Answer:
So the solution is
which approximates to
.
So the exact length is
units while the approximate length is
units.
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