Test 20
1.
\(ABCD\) square\(,\)\(\ |DE|=|EC|=6,\)\(\ 2|BF|=|CF|=8,\)\(\ m(\angle EAF)=x\)
\(\Rightarrow x=?\)
A) \(15^\circ\)B) \(30^\circ\)C) \(45^\circ\)D) \(60^\circ\)E) \(75^\circ\)
2.
\(ABCD\) trapezoid\(,\)\(\ |DC|=4,\)\(\ |AD|=4,\)\(\ |AB|=8,\)\(\ |BC|=7\)
\(\Rightarrow\cos C=?\)
A) \(\samefrac78\)B) \(\samefrac45\)C) \(1\)D) \(-\samefrac45\)E) \(-\samefrac78\)
3.
\(ABCD\) cyclic\(,\)\(\ |AB|=4,\)\(\ |AD|=3,\)\(\ |BC|=2,\)\(\ |DC|=2\)
\(\Rightarrow\cos C=?\)
A) \(-\samefrac18\)B) \(-\samefrac{15}{32}\)C) \(-\samefrac12\)D) \(-\samefrac{17}{32}\)E) \(-\samefrac{19}{32}\)
4.
\(ABCDEFGH\) cube\(,\)\(\ |KH|=2|EK|,\)\(\ m(\angle KBF)=\alpha\)
\(\Rightarrow\sin\alpha=?\)
A) \(\samefrac3{\sqrt{19}}\)B) \(\samefrac{\sqrt5}{\sqrt{19}}\)C) \(\samefrac{\sqrt{10}}{\sqrt{19}}\)D) \(\samefrac23\)E) \(\samefrac13\)
5.
\(ABCDEFGH\) rectangular prism\(,\)\(\ |BC|=3,\)\(\ |AB|=4,\)\(\ |GC|=2,\)\(\ m(\angle CAG)=\alpha\)
\(\Rightarrow\cos\alpha=?\)
A) \(\samefrac2{\sqrt5}\)B) \(\samefrac3{\sqrt5}\)C) \(\samefrac45\)D) \(\samefrac5{\sqrt{29}}\)E) \(\samefrac4{\sqrt{29}}\)
6.
\(a^2=b^2+c^2-bc\)
\(\Rightarrow\cos A=?\)
A) \(\samefrac12\)B) \(\samefrac{\sqrt2}{2}\)C) \(\samefrac{\sqrt3}{2}\)D) \(1\)E) \(-\samefrac{\sqrt2}{2}\)
7.
\(ABCD\) trapezoid\(,\)\(\ |DC|=4,\)\(\ |AD|=5,\)\(\ |AB|=9,\)\(\ |BC|=4\)
\(\Rightarrow\cos C=?\)
A) \(\samefrac12\)B) \(\samefrac25\)C) \(\samefrac5{\sqrt{21}}\)D) \(-\samefrac25\)E) \(-\samefrac12\)
8.
\(a\ne c,\ a^3-c^3=ab^2-cb^2\)
\(\Rightarrow\cos B=?\)
A) \(\samefrac12\)B) \(\samefrac{\sqrt3}{2}\)C) \(1\)D) \(-\samefrac{\sqrt3}{2}\)E) \(-\samefrac12\)