Test 26
1.
\(ABCD\) square\(,\)\(\ |DE|=1,\)\(\ |EC|=2,\)\(\ |FC|=2,\)\(\ |BF|=1,\)\(\ m(EAF)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(-\samefrac8{15}\)B) \(\samefrac18\)C) \(\samefrac34\)D) \(\samefrac43\)E) \(\samefrac8{15}\)
2.
The source figure consists of congruent squares; \(x\) is the marked angle.
\(\Rightarrow\cot x=?\)
A) \(\samefrac87\)B) \(\samefrac53\)C) \(\samefrac98\)D) \(\samefrac{10}{7}\)E) \(\samefrac54\)
3.
\(AB\perp BC,\)\(\ |AE|=1,\)\(\ |EB|=3,\)\(\ |BD|=2,\)\(\ |DC|=3,\)\(\ m(DFC)=\alpha\)
\(\Rightarrow\cot\alpha=?\)
A) \(\samefrac{11}{7}\)B) \(\samefrac25\)C) \(1\)D) \(\samefrac52\)E) \(\samefrac7{11}\)
4.
\(ABCD\) square\(,\)\(\ |AB|=|BE|,\)\(\ 3|BF|=|CF|,\)\(\ m(AHE)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(\samefrac35\)B) \(\samefrac53\)C) \(\samefrac52\)D) \(\samefrac25\)E) \(-\samefrac53\)
5.
\(AD\perp AB,\)\(\ BC\perp AB,\)\(\ |EB|=8,\)\(\ |BC|=6,\)\(\ |AD|=4,\)\(\ |AE|=3\)
\(\Rightarrow\sin(DEC)=?\)
A) \(\samefrac34\)B) \(\samefrac43\)C) \(\samefrac35\)D) \(1\)E) \(-\samefrac43\)
6.
\(ABC\) equilateral\(,\)\(\ |BD|=2|DC|,\)\(\ m(DAC)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(-\samefrac{\sqrt3}{5}\)B) \(-\samefrac1{\sqrt3}\)C) \(\samefrac1{\sqrt3}\)D) \(1\)E) \(\samefrac{\sqrt3}{5}\)
7.
\(|AC|=|BC|,\ \tan C=\samefrac43\)
\(\Rightarrow\tan A=?\)
A) \(\samefrac34\)B) \(\samefrac12\)C) \(2\)D) \(\samefrac43\)E) \(-\samefrac34\)
8.
\(AB\perp AC,\)\(\ |AB|=|AC|,\)\(\ |AD|=|DB|,\)\(\ |AE|=|EC|\)
\(\Rightarrow\cos x=?\)
A) \(-\samefrac35\)B) \(-\samefrac12\)C) \(-\samefrac13\)D) \(-\samefrac25\)E) \(-\samefrac45\)