Question

Найти углы треутольника АВС, если они относятся как 8к10 и12

Answer 1

Ответ:

48°, 60° и 72°

Объяснение:

Сумма внутренних углов треугольника равна 180 градусов.

Меньший угол равен 8*180/(8 + 10 + 12) = 48°

Больший угол равен 12*180/(8 + 10 + 12) = 72°

Третий угол равен 10*180/(8 + 10 + 12) = 60°

Answer 2

Сумма частей углов треугольника: 8+10+12=30;

Сумма углов треугольника: 180 градусов;

180/30=6° - величина одной части угла;

6*8=48° - один угол, 6*10=60° - второй угол, 6*12=72° - третий угол.

Answer 3

Finding the Angles of Triangle ABC

To find the angles of triangle ABC, we need to use the given information that the ratios of the angles are 8:10:12. Let's denote the angles of triangle ABC as A, B, and C, respectively.

According to the given ratios, we can write the following equation:

A:B:C = 8:10:12

To find the actual values of the angles, we need to determine the common ratio by dividing each ratio by their greatest common divisor (GCD). In this case, the GCD of 8, 10, and 12 is 2. Dividing each ratio by 2, we get:

A:B:C = 4:5:6

Now, we can assign variables to the angles:

A = 4x B = 5x C = 6x

where x is a constant.

Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:

A + B + C = 180

Substituting the values of A, B, and C, we get:

4x + 5x + 6x = 180

Simplifying the equation, we have:

15x = 180

Dividing both sides by 15, we find:

x = 12

Now, we can substitute the value of x back into the equations for A, B, and C:

A = 4x = 4 * 12 = 48 degrees B = 5x = 5 * 12 = 60 degrees C = 6x = 6 * 12 = 72 degrees

Therefore, the angles of triangle ABC are:

Angle A = 48 degrees Angle B = 60 degrees Angle C = 72 degrees

Please note that the above calculations are based on the given ratios and assumptions made. If there is any additional information or context provided, it may affect the calculations.