Test 26
1.
\(ABCD\text{ square},\ |DE|=1,\ |EC|=2,\ |FC|=2,\ |BF|=1,\ m(EAF)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(-\samefrac8{15}\)B) \(\samefrac18\)C) \(\samefrac34\)D) \(\samefrac43\)E) \(\samefrac8{15}\)
2.
\(\text{The source figure consists of congruent squares; }x\text{ is the marked angle.}\)
\(\Rightarrow\cot x=?\)
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.
\(ABCD\text{ square},\ |AB|=|BE|,\ 3|BF|=|CF|,\ m(AHE)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
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.
\(ABC\text{ equilateral},\ |BD|=2|DC|,\ m(DAC)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
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) \(-\samefrac45\)