2002 AMC 12P Problems/Problem 16
Problem
The altitudes of a triangle are and
The largest angle in this triangle is
Solution
Let and
denote the bases of altitudes
and
respectively. Since they are all altitudes and bases of the same triangle, they have the same area, so
Multiplying by
, we get
Notice that a simple solution to the equation is if all of them equal
That means
and
Simplifying our solution to check for Pythagorean triples we see that this is just a Pythagorean triple, namely a
triangle. Since the other two angles of a right triangle must be acute, the right angle must be the greatest angle. Therefore, our answer is
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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All AMC 12 Problems and Solutions |
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