Câu 9: Xét ΔABC có \(cosA=\dfrac{b^2+c^2-a^2}{2\cdot b\cdot c}\)
=>\(\dfrac{7^2+5^2-a^2}{2\cdot7\cdot5}=\dfrac{4}{5}\)
=>\(49+25-a^2=\dfrac{4}{5}\cdot2\cdot7\cdot5=56\)
=>\(a^2=49+25-56=18\)
=>\(a=3\sqrt{2}\)
=>Chọn A
Câu 10: Xét ΔABC có \(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)
=>\(cosA=\dfrac{4^2+9^2-7^2}{2\cdot4\cdot9}=\dfrac{48}{8\cdot9}=\dfrac{2}{3}\)
=>Chọn D
Câu 11: Xét ΔABC có \(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)
=>\(cosA=\dfrac{13^2+15^2-24^2}{2\cdot13\cdot15}=\dfrac{-7}{15}\)
=>\(\widehat{A}\simeq117^049'\)
=>Chọn B
Câu 12: Xét ΔABC có \(cosB=\dfrac{BA^2+BC^2-AC^2}{2\cdot BA\cdot BC}\)
=>\(cosB=\dfrac{15^2+13^2-14^2}{2\cdot15\cdot13}=\dfrac{33}{65}\)
=>\(\widehat{B}\simeq59^029'\)
=>Chọn C