Test 8
1.
\(ABCD\text{ is a square, }E\in DC,\ |DE|=3|EC|,\ m(\angle EAB)=x\)
\(\cot x=?\)
A) \(\samefrac43\)B) \(\samefrac45\)C) \(\samefrac35\)D) \(\samefrac34\)E) \(\samefrac14\)
2.
\(AB\perp BC,\ |BC|=12,\ \cos\alpha=\samefrac35\)
\(\Rightarrow\text{Perimeter}(ABC)=?\)
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.
\(ABCD\text{ is a rectangle, }E\in AB,\ \cot\theta=4,\ \tan\alpha=2,\ |AB|=9\)
\(\Rightarrow |CE|=?\)
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) \(2\)