Difference between revisions of "1979 AHSME Problems/Problem 3"
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Notice that <math>\measuredangle DAE = 90^\circ+60^\circ = 150^\circ</math> and that <math>AD = AE</math>. Then triangle <math>ADE</math> is isosceles, so <math>\measuredangle AED = \dfrac{180^\circ-150^\circ}{2} = \boxed{\textbf{(C) } 15}</math>. | Notice that <math>\measuredangle DAE = 90^\circ+60^\circ = 150^\circ</math> and that <math>AD = AE</math>. Then triangle <math>ADE</math> is isosceles, so <math>\measuredangle AED = \dfrac{180^\circ-150^\circ}{2} = \boxed{\textbf{(C) } 15}</math>. | ||
+ | == Solution 2 (Obnoxiously tedious) == | ||
+ | |||
+ | WLOG, let the side length of the square and the equilateral triangle be <math>1</math>. <math>\angle{DAE}=90^\circ+60^\circ=150^\circ. Apply the law of cosines then the law of sines, we find that </math>\angle{AED}=15^\circ<math>. Select </math>\boxed{C}$. | ||
+ | |||
+ | ~hastapasta | ||
== Video Solution == | == Video Solution == | ||
https://youtu.be/FDgcLW4frg8?t=1341 | https://youtu.be/FDgcLW4frg8?t=1341 |
Revision as of 13:07, 3 May 2022
Contents
[hide]Problem 3
In the adjoining figure, is a square, is an equilateral triangle and point is outside square . What is the measure of in degrees?
Solution
Solution by e_power_pi_times_i
Notice that and that . Then triangle is isosceles, so .
Solution 2 (Obnoxiously tedious)
WLOG, let the side length of the square and the equilateral triangle be . \angle{AED}=15^\circ\boxed{C}$.
~hastapasta
Video Solution
https://youtu.be/FDgcLW4frg8?t=1341
~ pi_is_3.14
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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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