Question

В равнобедренном треугольнике АВС угол В=120 градусов,боковое ребро равно 10 см,основание равно 8 см,найти площадь треугольника Заранее спасибо!!!

Answer 1

Calculation of the Area of an Isosceles Triangle

To find the area of a triangle, we can use the formula:

Area = (base * height) / 2

In this case, we have an isosceles triangle ABC, where angle B is 120 degrees, the side length is 10 cm, and the base is 8 cm.

To find the height of the triangle, we can use the formula:

height = side * sin(angle)

Let's calculate the height first:

height = 10 cm * sin(120 degrees)

To calculate the sine of 120 degrees, we can use a calculator or refer to a trigonometric table. However, since we don't have access to a calculator or table, we can use an approximation. The sine of 120 degrees is approximately 0.866.

height ≈ 10 cm * 0.866 ≈ 8.66 cm

Now that we have the height, we can calculate the area of the triangle:

Area = (8 cm * 8.66 cm) / 2 ≈ 34.64 cm²

Therefore, the area of the triangle ABC is approximately 34.64 square centimeters.

Please note that the calculations provided are based on the given information and approximations.