Предмет: Геометрия, автор: valentinazozulyaw

із точки до прямої проведено,дві похилі довжини, яких відносяться, як 5:6,а проекції цих похилих на пряму дорівнюють 7см і 18 см. Знайдіть довжини цих похилих та відстань від точки до прямої.

Ответы

Автор ответа: oleksa43d

Ответ:

Довжина одной наклонной l₁ = 5x, и её проекция p₁ = 7 см

Длина второй наклонной l₂ = 6x, и её проекция p₂ = 18 см

Высота h

Теорема Пифагора для одной и для второй наклонной

l₁² = h² + p₁²

l₂² = h² + p₂²

---

(5x)² = h² + 7²

(6x)² = h² + 18²

---

25x² = h² + 49

36x² = h² + 324

вычтем первое из второго

(36 - 25)x² = 324 - 49

11x² = 375

x² = 25

x = 5 см

(5x)² = h² + 7²

25² = h² + 7²

h² = 25² - 7² = (25+7)(25-7) = 32*18 = 16*36

h = 4*6 = 24 см

valentinazozulyaw: спасибо

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