Question

Треугольник АБС угол А равен 60 градусов АВ равен 12 АС равен 8 найти SАВС

Answer 1

Площадь треугольника равна половине произведения двух сторон на синус угла между ними:
S (ABC) = 1/2 AB*AC*sin∠A = 1/2*12*8*√3/2 = 24√3

Answer 2

Finding the Area of Triangle ABC

To find the area of triangle ABC, we can use the formula for the area of a triangle: Area = (1/2) * base * height. In this case, we need to determine the base and height of triangle ABC.

Given: - Angle A is equal to 60 degrees. - Side AB is equal to 12. - Side AC is equal to 8.

To find the height of triangle ABC, we can use trigonometry. Since angle A is 60 degrees, we can use the sine function to find the height. The height will be the side opposite to angle A.

Using the sine function: sin(A) = opposite/hypotenuse, we can rearrange the formula to solve for the height: height = AB * sin(A).

Let's calculate the height of triangle ABC using the given values: height = 12 * sin(60) = 12 * 0.866 = 10.392.

Now that we have the height, we can calculate the area of triangle ABC using the formula: Area = (1/2) * base * height.

Substituting the values: Area = (1/2) * 8 * 10.392 = 41.568 square units.

Therefore, the area of triangle ABC is 41.568 square units.

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