Question

Answer 1

19.C

20.D

21.A

22.B

23.C

24.B

26.C

28.D

Answer 2

31D

32A

33C

29:

\(sinB=\sqrt{1-\dfrac{1}{64}}=\sqrt{\dfrac{63}{64}}=\dfrac{3\sqrt{7}}{8}\)

\(sinC=\sqrt{1-\dfrac{9}{16}}=\sqrt{\dfrac{7}{16}}=\dfrac{\sqrt{7}}{4}\)

\(sin\left(B+C\right)=sinB\cdot cosC+sinC\cdot cosB\)

\(=\dfrac{3\sqrt{7}}{8}\cdot\dfrac{3}{4}+\dfrac{1}{8}\cdot\dfrac{\sqrt{7}}{4}=\dfrac{10\sqrt{7}}{32}=\dfrac{5\sqrt{7}}{16}\)

=>\(sinA=\dfrac{5\sqrt{7}}{16}\)

\(\dfrac{BC}{sinA}=\dfrac{AC}{sinB}\)

=>\(BC:\dfrac{5\sqrt{7}}{16}=6:\dfrac{3\sqrt{7}}{8}=\dfrac{48}{3\sqrt{7}}=\dfrac{16}{\sqrt{7}}\)

=>\(BC=\dfrac{16}{\sqrt{7}}\cdot\dfrac{5\sqrt{7}}{16}=5\)