Question

Найти Куты треугольника АВС если кут А в четыре раза меньше кута В и на 54 гр меньше кута С

Answer 1

Нехай кут А = х. Тоді за умовою кут В = 4х, а кут С = х + 54.
Сума кутів трикутника 180°,отже,
х+4х+х+54=180,
6х+54=180,
6х=126,
х=21.
Кут А = 21°, кут В = 4·21= 84°, кут С= 21+54= 75°.
Відповідь: 21°;  84°,  75°.

Answer 2

Finding the Angles of Triangle ABC

To find the angles of triangle ABC, we are given the following information: - Angle A is four times smaller than angle B. - Angle A is 54 degrees smaller than angle C.

Let's assign variables to the angles: - Angle A = x - Angle B = 4x (since angle A is four times smaller than angle B) - Angle C = x + 54 (since angle A is 54 degrees smaller than angle C)

To find the values of x, angle A, angle B, and angle C, we can set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees.

The equation is: x + 4x + (x + 54) = 180

Simplifying the equation: 6x + 54 = 180 6x = 180 - 54 6x = 126 x = 126 / 6 x = 21

Now that we have the value of x, we can find the values of angle A, angle B, and angle C: - Angle A = x = 21 degrees - Angle B = 4x = 4 * 21 = 84 degrees - Angle C = x + 54 = 21 + 54 = 75 degrees

Therefore, the angles of triangle ABC are: - Angle A = 21 degrees - Angle B = 84 degrees - Angle C = 75 degrees

Note: The values of the angles are based on the given information and the calculations performed.