Question

AB=BC AB=10cm B=72° Найти: АС

Answer 1

Решение на рисунке.
Использовано: сумма углов в треугольнике, теорема синусов, таблица Брадиса или калькулятор для вычисления значения синусов.

Answer 2

To find AC (the length of side AC), we need to use trigonometry, specifically the Law of Sines since we have an angle-side-angle (ASA) scenario.

The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C)

where: a, b, c are the side lengths of the triangle opposite to angles A, B, and C, respectively. A, B, C are the angles of the triangle opposite to sides a, b, and c, respectively.

In our case: AB = AC = 10 cm (opposite to angles A and C, respectively) B = 72° (angle B)

Now, we can set up the equation and solve for AC:

AC/sin(A) = AB/sin(B)

AC/sin(A) = 10 cm / sin(72°)

Next, we need to find angle A. Since the sum of the angles in a triangle is 180°, we can use the following formula to find angle A:

A = 180° - (B + C) A = 180° - (72° + 72°) A = 36°

Now we can plug the values into the equation:

AC/sin(36°) = 10 cm / sin(72°)

To solve for AC, rearrange the equation:

AC = (10 cm * sin(36°)) / sin(72°)

Now, use a calculator to find the value of AC:

AC ≈ (10 cm * 0.5878) / 0.9511 AC ≈ 5.878 cm / 0.9511 AC ≈ 6.18 cm

Therefore, the length of side AC is approximately 6.18 cm.