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Вопрос по геометрии
Анонимный
1 год назад

У прямокутному трикутнику катет дорівнює 3 см, а гострий кут, прилеглий до нього, - 35°. Знайди інший катет і гіпотенузу.
75 баллов ​

Ответы 1

Дано:

Катет AB = 3 см.

Кут A = 35°.


За визначенням синуса кута:

sin(A) = протилежний катет / гіпотенузаsin
(A) = BC / AC
sin(35°) = BC / AC
sin(35°) ≈ 0.5736

0.5736 = BC / AC

AB^2 + BC^2 = AC^2
3^2 + BC^2 = AC^2
9 + BC^2 = AC^2

Тепер у нас є два рівняння з двома невідомими (BC і AC). Давайте розв'яжемо їх.

Рівняння
sin(35°) = BC / AC:

0.5736 = BC / AC
BC / AB = AC / BC
BC / 3 = AC / BC
BC^2 = AC * 3

Рівняння 9 + BC^2 = AC^2

Тепер у нас є два рівняння з двома невідомими:

0.5736 = BC / AC

BC^2 = AC * 3

9 + BC^2 = AC^2

Відповідь: BC ≈ 1.706 см; Гіпотенуза дорівнює приблизно 3.47 см.

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