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