1988 AIME Problems/Problem 7

Problem

In triangle $ABC$ , $\tan \angle CAB = 22/7$ , and the altitude from $A$ divides $BC$ into segments of length 3 and 17. What is the area of triangle $ABC$ ?

Solution

Call $\angle BAD$ $\alpha$ and $\angle CAD$ $\beta$ . So, $\tan \alpha = \frac {17}{h}$ and $\tan \beta = \frac {3}{h}$ . Using the tangent addition formula $\tan (\alpha + \beta) =$ \frac {\tan \alpha + \tan \beta}{1 - \tan \alpha \cdot \tan \ beta} $, we get$ \frac {\frac {20}{h}}{\frac {x^2 - 51}{x^2}}$.

1988 AIME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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1988 AIME Problems/Problem 7

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