Test 22
1.
\(|AB|=4\sqrt3,\)\(\ |BC|=6,\)\(\ m(B)=30^\circ,\)\(\ m(A)=\alpha\)
\(\Rightarrow\sin\alpha=?\)
A) \(1\)B) \(\samefrac12\)C) \(\samefrac{\sqrt3}{2}\)D) \(\samefrac{\sqrt2}{2}\)E) \(\samefrac34\)
2.
\(|AB|=4\sqrt2,\)\(\ |AC|=6,\)\(\ m(A)=45^\circ\)
\(\Rightarrow A(ABC)=?\)
A) \(12\)B) \(16\)C) \(20\)D) \(24\)E) \(32\)
3.
\(|AB|=6,\)\(\ |AC|=4,\)\(\ m(B)=65^\circ,\)\(\ m(C)=85^\circ\)
\(\Rightarrow A(ABC)=?\)
A) \(6\)B) \(8\)C) \(12\)D) \(16\)E) \(24\)
4.
\(m(BAC)=120^\circ,\)\(\ |AB|=4,\)\(\ |AC|=x,\)\(\ A(ABC)=6\sqrt3\)
\(\Rightarrow x=?\)
A) \(4\)B) \(6\)C) \(6\sqrt3\)D) \(8\)E) \(8\sqrt3\)
5.
\(|AB|=5,\)\(\ |BC|=13,\)\(\ |CD|=13,\)\(\ |CE|=10,\)\(\ \angle BAC=90^\circ\)
\(\Rightarrow A(CDE)=?\)
A) \(90\)B) \(65\)C) \(30\)D) \(25\)E) \(9\)
6.
\(|AB|=8,\)\(\ |AC|=4,\)\(\ |BD|=|DC|,\)\(\ m(BAD)=30^\circ,\)\(\ m(DAC)=\alpha\)
\(\Rightarrow\sin\alpha=?\)
A) \(1\)B) \(\samefrac13\)C) \(\samefrac14\)D) \(\samefrac23\)E) \(\samefrac34\)
7.
\(|BD|=|DC|,\)\(\ |AB|=4\sqrt2,\)\(\ |AC|=8,\)\(\ m(BAD)=45^\circ,\)\(\ m(DAC)=x\)
\(\Rightarrow\sin x=?\)
A) \(\samefrac12\)B) \(\samefrac23\)C) \(\samefrac25\)D) \(\samefrac34\)E) \(\samefrac35\)
8.
\(|AC|=6,\ |BC|=4,\ |CD|=8,\ |CE|=12\)
\(\Rightarrow\samefrac{A(ABC)}{A(CDE)}=?\)
A) \(2\)B) \(3\)C) \(4\)D) \(\samefrac12\)E) \(\samefrac14\)