1989 AHSME Problems/Problem 15
Contents
[hide]Problem
In , , , , and is on with . Find the ratio of .
Solution
Drop the altitude from through , and let be . Then by Pythagoras and after subtracting the first equation from the second, . Therefore the desired ratio is
Solution 2 (Trig)
Using laws of cosines on yields Let Using laws of cosines on yields Fortunately, we know that Plugging this information back into our equation yields Then, we know that
See also
1989 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.