2008 iTest Problems/Problem 66
Problem
Michael draws in the sand such that
and
. He then picks a point at random from within the triangle and labels it point
. Next, he draws a segment from
to
that passes through
, hitting
at a point he labels
. Just then, a wave washes over his work, so Michael redraws the exact same diagram farther from the water, labeling all the points the same way as before. If hypotenuse
is
feet in length, let
be the probability that the number of feet in the length of
is less than
. Compute
.
Solution
Let be a point on
such that
feet. By using the definitions of sine and cosine,
feet and
feet. From the Pythagorean Theorem,
feet.
If the number of feet in the length of is less than
then point
is within the line segment
making point
inside
Since
and
the probability
is equal to
That means We can find
easily by using a calculator, but if we do not, note that
making
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 65 |
Followed by: Problem 67 | |
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