MathDB
Finding the Side Length of a Triangle

Source:

March 8, 2009

Problem Statement

In ABC \triangle ABC, we have \angle C \equal{} 3 \angle A, a \equal{} 27, and c \equal{} 48. What is b b?
[asy]size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair A=origin, B=(14,0), C=(10,6); draw(A--B--C--cycle); label("AA", A, SW); label("BB", B, SE); label("CC", C, N); label("aa", B--C, dir(B--C)*dir(-90)); label("bb", A--C, dir(C--A)*dir(-90)); label("cc", A--B, dir(A--B)*dir(-90)); [/asy]
<spanclass=latexbold>(A)</span> 33<spanclass=latexbold>(B)</span> 35<spanclass=latexbold>(C)</span> 37<spanclass=latexbold>(D)</span> 39<spanclass=latexbold>(E)</span> not uniquely determined <span class='latex-bold'>(A)</span>\ 33 \qquad <span class='latex-bold'>(B)</span>\ 35 \qquad <span class='latex-bold'>(C)</span>\ 37 \qquad <span class='latex-bold'>(D)</span>\ 39 \qquad <span class='latex-bold'>(E)</span>\ \text{not uniquely determined}