# Difference between revisions of "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 .
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