Test 21
1.
\(|AB|=4\sqrt3,\ |AC|=4,\ m(B)=30^\circ\)
\(\Rightarrow m(C)=?\)
A) \(15^\circ\)B) \(30^\circ\)C) \(45^\circ\)D) \(60^\circ\)E) \(75^\circ\)
2.
\(m(BAC)=75^\circ,\ m(ABC)=45^\circ,\ |AC|=6\)
\(\Rightarrow |AB|=?\)
A) \(3\sqrt2\)B) \(3\sqrt6\)C) \(10\)D) \(6\sqrt3\)E) \(15\)
3.
\(O\text{ center},\ m(A)=60^\circ,\ |OC|=4\sqrt3\)
\(\Rightarrow |BC|=?\)
A) \(4\)B) \(6\)C) \(6\sqrt3\)D) \(12\)E) \(12\sqrt3\)
4.
\(O\text{ center},\ m(A)=45^\circ,\ |BC|=4\sqrt2\)
\(\Rightarrow R=?\)
A) \(2\)B) \(4\)C) \(6\)D) \(8\)E) \(10\)
5.
\(O\text{ center},\ m(B)=30^\circ,\ |OC|=8\)
\(\Rightarrow |AC|=x=?\)
A) \(4\)B) \(6\)C) \(8\)D) \(12\)E) \(16\)
6.
\(|AC|=3,\ |AB|=9,\ m(ABC)=\alpha,\ m(BCA)=90^\circ+\alpha\)
\(\Rightarrow\sin\alpha=?\)
A) \(\samefrac14\)B) \(\samefrac1{\sqrt{10}}\)C) \(\samefrac3{\sqrt{10}}\)D) \(\samefrac3{\sqrt{10}}\)E) \(\samefrac12\)
7.
\(|AB|=15,\ |AC|=20,\ \angle A=90^\circ,\ m(ADB)=120^\circ\)
\(\Rightarrow |AD|=?\)
A) \(4\sqrt3\)B) \(6\sqrt3\)C) \(6\)D) \(8\sqrt3\)E) \(8\)
8.
\(|AB|=8,\ |AC|=6,\ |BD|=|DC|,\ m(BAD)=30^\circ,\ m(DAC)=x\)
\(\Rightarrow\sin x=?\)
A) \(\samefrac12\)B) \(\samefrac13\)C) \(\samefrac23\)D) \(\samefrac34\)E) \(\samefrac35\)