Question

Две стороны треугольника равны 12см и 9см а угол между ними равен 30 градусов найдите площадь треугольника

Answer 1

Площадь треугольника можно вычислить по формуле S=1/2*a*b*sin(C), где a,b - две стороны треугольника, С - угол между ними.

В нашем случае S=1/2*12*9*1/2=27см²

Answer 2

Problem Analysis

We are given a triangle with two sides measuring 12 cm and 9 cm, and the angle between them is 30 degrees. We need to find the area of the triangle.

Solution

To find the area of the triangle, we can use the formula: Area = (1/2) * base * height.

In this case, the two given sides of the triangle are the base and height. Let's label the sides as follows: - Side A = 12 cm (base) - Side B = 9 cm (height) - Angle C = 30 degrees (angle between sides A and B)

To find the area, we need to calculate the length of the base and height. We can use trigonometric functions to do this.

Using trigonometry, we can determine that the height of the triangle is given by height = side B * sin(angle C).

Substituting the given values, we have: - height = 9 cm * sin(30 degrees)

To find the base of the triangle, we can use the Pythagorean theorem. The base is the hypotenuse of a right triangle formed by the given sides. Let's label the third side as side C.

Using the Pythagorean theorem, we have: - side C^2 = side A^2 - side B^2 - side C^2 = 12 cm^2 - 9 cm^2 - side C^2 = 144 cm^2 - 81 cm^2 - side C^2 = 63 cm^2

Taking the square root of both sides, we find: - side C = √63 cm

Now that we have the base and height, we can calculate the area of the triangle using the formula mentioned earlier: - Area = (1/2) * base * height - Area = (1/2) * 12 cm * 9 cm * sin(30 degrees)

Let's calculate the area using the given values.

Calculation

- height = 9 cm * sin(30 degrees) = 9 cm * 0.5 = 4.5 cm - base = √63 cm

Now, we can calculate the area: - Area = (1/2) * 12 cm * 4.5 cm = 54 cm^2

Answer

The area of the triangle is 54 cm^2.

Conclusion

In this problem, we were given a triangle with two sides measuring 12 cm and 9 cm, and the angle between them was 30 degrees. We used trigonometry to calculate the height of the triangle and the Pythagorean theorem to find the base. Finally, we used the formula for the area of a triangle to calculate the area, which was found to be 54 cm^2.