1979 AHSME Problems/Problem 20
Problem #20
If and then the radian measure of equals
Solution
Solution by e_power_pi_times_i
Since , . Now we evaluate and . Denote and such that . Then , and simplifying gives . So and . The question asks for , so we try to find in terms of and . Using the angle addition formula for , we get that . Plugging and in, we have . Simplifying, , so in radians is .
Solution 1.1 (Guiding through the thought process)
Thinking through the problem, we can see is the angle whose tangent is . is the angle whose tangent is . Call the former angle , the latter . So we are trying to find . So given two tangent measures, it is natural for us to think about the sum of tangent measures (what else can we try? Remember: we are not allowed to use calculators). Plug in as above and continue on.
~hastapasta
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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