Difference between revisions of "1989 AHSME Problems/Problem 15"
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== Solution 2 (Trig) == | == Solution 2 (Trig) == | ||
− | Using laws of cosines on <math>\bigtriangleup ABC</math> yields <math>49=25+81-2 \cdot 5 \cdot 9 \cdot \cos A | + | Using laws of cosines on <math>\bigtriangleup ABC</math> yields <math>49=25+81-2 \cdot 5 \cdot 9 \cdot \cos A</math> |
== See also == | == See also == |
Revision as of 17:59, 21 June 2020
Contents
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
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.