Test 25
1.
\(AB\perp BC,\)\(\ |AD|=1,\)\(\ |DB|=2,\)\(\ |BC|=2,\)\(\ m(DCA)=x\)
\(\Rightarrow\tan x=?\)
A) \(\samefrac1{10}\)B) \(\samefrac2{10}\)C) \(\samefrac3{10}\)D) \(\samefrac15\)E) \(\samefrac25\)
2.
\(ABCD\) square\(,\)\(\ |AB|=3|CE|,\)\(\ m(CAE)=\alpha\)
\(\Rightarrow\cot\alpha=?\)
A) \(7\)B) \(\samefrac25\)C) \(\samefrac15\)D) \(\samefrac52\)E) \(\samefrac17\)
3.
\(ABCD\) square\(,\)\(\ E\in AD,\)\(\ 2|AE|=|ED|,\)\(\ m(EBD)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(\samefrac13\)B) \(\samefrac12\)C) \(\samefrac23\)D) \(3\)E) \(4\)
4.
\(AB\perp BC,\)\(\ |AD|=|DC|,\)\(\ \tan(ADB)=\samefrac43,\)\(\ m(DAC)=\alpha\)
\(\Rightarrow\cot\alpha=?\)
A) \(\samefrac12\)B) \(\samefrac23\)C) \(\samefrac14\)D) \(\samefrac34\)E) \(2\)
5.
\(ABCD\) and \(BEFG\) are squares\(,\)\(\ |AB|=2|BE|\)
\(\Rightarrow\tan(AGE)=?\)
A) \(3\)B) \(-\samefrac32\)C) \(-\samefrac12\)D) \(-\samefrac23\)E) \(-3\)
6.
\(ABCD\) rectangle\(,\)\(\ |AE|=|EF|=|FB|,\)\(\ |AD|=3|AE|\)
\(\Rightarrow\tan\alpha=?\)
A) \(-\samefrac1{2\sqrt3}\)B) \(-\samefrac5{12}\)C) \(-\samefrac{12}{5}\)D) \(\samefrac5{12}\)E) \(\samefrac{12}{5}\)
7.
\(ABCD\) square\(,\)\(\ |DE|=|EC|;\)\(\ \alpha\) is the marked intersection angle
\(\Rightarrow\cot\alpha=?\)
A) \(\samefrac13\)B) \(\samefrac25\)C) \(\samefrac12\)D) \(\samefrac52\)E) \(3\)
8.
\(ABCD\) square\(,\)\(\ 2|DE|=|AE|,\)\(\ m(BEC)=x\)
\(\Rightarrow\cot x=?\)
A) \(1\)B) \(\samefrac79\)C) \(\samefrac97\)D) \(\samefrac{19}{25}\)E) \(\samefrac{25}{19}\)