右図のような四角形ABCDがある．各辺の長さは，$\text{AB}=11,\ \text{BC}=10,\ \text{CD}=5,\ \text{DA}=4$であり，対角線ACの長さは6である．2つの対角線ACとBDの交点をEとし，$\angle \text{ACB}=\alpha,\ \angle \text{ACD}=\beta$とする．
(1) $\cos \alpha,\ \sin \alpha,\ \cos \beta,\ \sin \beta$の値を求めよ．
(2) $\cos (\alpha+\beta)$の値，および対角線BDの長さを求めよ．
(3) CEの長さを求めよ．
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