Предмет: Геометрия, автор: ponnnnnn727282

у трикутнику АВС знайдіть кут В якщо С=90°, А:В=2:7
будь-ласочка даю 20 балів

Ответы

Автор ответа: mariyamir

Ответ:

З огляду на те, що С=90°, трикутник АВС є прямокутним трикутником.

За теоремою про суму кутів в трикутнику, сума всіх кутів трикутника дорівнює 180°. Оскільки один з кутів дорівнює 90°, то залишкові два кути мають суму 90°.

З огляду на те, що відношення між кутами А та В становить 2:7, ми можемо записати, що:

А:В = 2:7

Це означає, що кут А складає 2/9 всієї суми двох залишкових кутів, а кут В складає 7/9 всієї суми двох залишкових кутів.

Таким чином, ми можемо записати:

А = (2/9) * 90° = 20°

В = (7/9) * 90° = 70°

Отже, кут В дорівнює 70°.

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