1980 AHSME Problems/Problem 12
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 12 | |
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