1993 AHSME Problems/Problem 23
Problem
Points and are on a circle of diameter , and is on diameter
If and , then
Solution
We have all the angles we need, but most obviously, we see that right angle in triangle .
Note also that angle is 6 degrees, so length because the diameter, , is 1.
Now, we can concentrate on triangle (after all, now we can decipher all angles easily and use Law of Sines).
We get:
That's equal to
Therefore, our answer is equal to:
Note that , and don't accidentally put because you thought was !
See also
1993 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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