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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