Test 8
1.
\(ABCD\) is a square, \(E\in DC,\)\(\ |DE|=3|EC|,\)\(\ m(\angle EAB)=x\)
\(\cot x=?\)
A) \(\samefrac43\)B) \(\samefrac45\)C) \(\samefrac35\)D) \(\samefrac34\)E) \(\samefrac14\)
2.
\(AB\perp BC,\)\(\ |BC|=12,\)\(\ \cos\alpha=\samefrac35\)
\(\Rightarrow\)Perimeter\((ABC)=?\)
A) \(12\)B) \(24\)C) \(36\)D) \(40\)E) \(48\)
3.
\(AB\perp BC,\)\(\ |AC|=10,\)\(\ \tan\alpha=\samefrac12\)
\(\Rightarrow |AB|+|BC|=?\)
A) \(2\sqrt5\)B) \(4\sqrt5\)C) \(6\sqrt5\)D) \(10\)E) \(20\)
4.
\(ABCD\) is a rectangle, \(E\in AB,\)\(\ \cot\theta=4,\)\(\ \tan\alpha=2,\)\(\ |AB|=9\)
\(\Rightarrow |CE|=?\)
A) \(\sqrt5\)B) \(2\sqrt5\)C) \(3\sqrt5\)D) \(4\sqrt5\)E) \(6\sqrt5\)
5.
\(AB\perp BC,\)\(\ DE\perp EC,\)\(\ |AB|=36,\)\(\ |BD|=22,\)\(\ m(\angle EDC)=\alpha,\)\(\ \tan\alpha=\samefrac34\)
\(\Rightarrow |EC|=?\)
A) \(3\)B) \(4\)C) \(6\)D) \(9\)E) \(12\)
6.
\(AD\perp BC,\)\(\ |AD|=12,\)\(\ |BC|=25,\)\(\ 16\tan B=9\tan C\)
\(\Rightarrow |AB|=?\)
A) \(20\)B) \(15\)C) \(14\)D) \(12\)E) \(10\)
7.
\(AH\perp BC,\)\(\ |AH|=12,\)\(\ |BC|=16\)
\(\Rightarrow\cot B+\cot C=?\)
A) \(\samefrac43\)B) \(\samefrac83\)C) \(3\)D) \(4\)E) \(6\)
8.
\(|AB|=|AC|,\)\(\ \sin A=\samefrac45\)
\(\Rightarrow\cot C=?\)
A) \(\samefrac12\)B) \(\samefrac45\)C) \(\samefrac43\)D) \(1\)E) \(2\)