Difference between revisions of "1980 AHSME Problems/Problem 12"
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[[Category: Introductory Algebra Problems]] | [[Category: Introductory Algebra Problems]] | ||
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Latest revision as of 18:02, 20 March 2018
Problem
The equations of and are and , respectively. Suppose makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does , and that has 4 times the slope of . If is not horizontal, then is
Solution
Solution by e_power_pi_times_i
, as stated in the question. In the line , draw a triangle with the coordinates , , and . Then . Similarly, . Since and , . Using the angle addition formula for tangents, . Solving, we have . But line is not horizontal, so therefore . Looking at the answer choices, it seems the answer is .
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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 |
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