Question

В треугольнике АВС угол С равен 90, АС=9, sinB=3/5. Найдите ВС.

Answer 1

По теореме Пифагора: $AB=sqrt{AB^2-BC^2}$

$BC=sqrt{AB^2-AC^2};$

$sinB=frac{AC}{AB}</var>;$<br /><br /><img src=[/tex]AB=frac{AC}{sinB};" title="sinB=frac{AC}{AB};" title="AB=frac{AC}{sinB};" title="sinB=frac{AC}{AB};" alt="AB=frac{AC}{sinB};" title="sinB=frac{AC}{AB};" />

$sinB=frac{AC}{AB}</var>;$

$<var>AB=frac{AC}{sinB};$

$<var>AB=frac{9}{frac{3}{5}}=frac{9*5}{3}=15</var>;" title="<var>AB=frac{AC}{sinB};" /> [tex]<var>AB=frac{9}{frac{3}{5}}=frac{9*5}{3}=15</var>;" alt="<var>AB=frac{AC}{sinB};" /> [tex]<var>AB=frac{9}{frac{3}{5}}=frac{9*5}{3}=15</var>;" /> [tex]<var>CB=sqrt{15^2-9^2}=sqrt{144}=12</var>;$

Ответ: $<var>CB=12</var>.$