Question

Знайдіть гострі кути прямокутного трикутника, якщо їх градусні міри відносяться як 4 : 11.​

Answer 1

Ответ: 24° и 66°

Объяснение:

сумма острых углов составляет 90°, поэтому, обозначив коэффициент пропорциональности как х, найдем эти углы, и сложим их, получим уравнение

4х+11х=90, х=90/15; х=6, значит, один угол 6°*4=24°, а другой 11*6°=66°

Answer 2

Finding the acute angles of a right triangle

To find the acute angles of a right triangle, we need to know the ratio of their degree measures. In this case, the ratio of the degree measures of the acute angles is given as 4:11.

Let's assume that one acute angle measures x degrees. According to the given ratio, the other acute angle would measure 11x degrees.

Since we are dealing with a right triangle, we know that the sum of the degree measures of the acute angles is always 90 degrees. Therefore, we can set up the following equation:

x + 11x = 90

Simplifying the equation, we get:

12x = 90

Dividing both sides of the equation by 12, we find:

x = 7.5

So, one acute angle of the right triangle measures 7.5 degrees, and the other acute angle measures 11 times that, which is:

11 * 7.5 = 82.5 degrees.

Therefore, the acute angles of the right triangle, with a ratio of 4:11, measure approximately 7.5 degrees and 82.5 degrees.