MathDB
1987 AMC 12 #14 - Angle in a Square

Source:

December 31, 2011
trigonometryPythagorean TheoremgeometryAMC

Problem Statement

ABCDABCD is a square and MM and NN are the midpoints of BCBC and CDCD respectively. Then sinθ=\sin \theta= [asy] draw((0,0)--(2,0)--(2,2)--(0,2)--cycle); draw((0,0)--(2,1)); draw((0,0)--(1,2)); label("A", (0,0), SW); label("B", (0,2), NW); label("C", (2,2), NE); label("D", (2,0), SE); label("M", (1,2), N); label("N", (2,1), E); label("θ\theta", (.5,.5), SW); [/asy] <spanclass=latexbold>(A)</span> 55<spanclass=latexbold>(B)</span> 35<spanclass=latexbold>(C)</span> 105<spanclass=latexbold>(D)</span> 45<spanclass=latexbold>(E)</span> none of these <span class='latex-bold'>(A)</span>\ \frac{\sqrt{5}}{5} \qquad<span class='latex-bold'>(B)</span>\ \frac{3}{5} \qquad<span class='latex-bold'>(C)</span>\ \frac{\sqrt{10}}{5} \qquad<span class='latex-bold'>(D)</span>\ \frac{4}{5} \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}