Биссектриса одного из углов прямоугольника делит одну из его сторон на два отрезка длины которых 12 и 8 см . вычислите длины сторон прямоугольника

ABCD-прямоугольник,
AE-биссектриса делит сторону ВС на 
ВЕ=8 и ЕС=12
значит сторона ВС=12+8=20 см.
Биссектриса АЕ разбивает прямой угол на 2 по 45 градусов, поэтому треугольник АВЕ- равнобедренный прямоугольник, а значит 
если ВЕ=8 см, то АВ=8см
или же ВЕ=12см ,то и АВ=12 см.
ответ: 1 сторона- 20 см, 2 сторона - 8 см или 12 см

Основное тригонометрическое тождество:

sin²α + cos²α = 1,      откуда

sinα = √(1 - cos²α)  или  sinα = - √(1 - cos²α)

Знак синуса зависит от координатной четверти, в которой расположен угол.

Но в данной задаче, вероятно, речь идет об остром угле прямоугольного треугольника, поэтому будем рассматривать синус угла только положительный.

tgα = sinα / cosα

1. cosα = 5/13

sinα = √(1 - 25/169) = √(144/169) = 12/13

tgα = 12/13 : 5/13 = 12/5

2. cosα = 15/17

sinα = √(1 - 225/289) = √(64/289) = 8/17

tgα = 8/17 : 15/17 = 8/15

3. cosα = 0,6

sinα = √(1 - 0,36) = √(0,64 ) = 0,8

tgα = 0,8/0,6 = 8/6 = 4/3

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