Question

Найдите площадь треугольника одна из сторон равна 12 а прилежащие к ней углы 30 и 75

Answer 1

Третий угол равен 180-105=75 градусов,поэтому в треугольнике две равные строны по 12 см,с углом между с ними 30 градусов. Площадь равна:144/4=36 кв.см.

Answer 2

Calculation of the Triangle's Area

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

Area = (1/2) * base * height

In this case, we are given that one side of the triangle is 12 units long, and the adjacent angles are 30 degrees and 75 degrees.

To find the height of the triangle, we can use trigonometry. Since we know the length of one side and the measure of the adjacent angle, we can use the sine function to find the height.

Let's calculate the height using the given information:

1. Convert the angle measures from degrees to radians: - Angle 1: 30 degrees = 30 * (π/180) radians - Angle 2: 75 degrees = 75 * (π/180) radians

2. Use the sine function to find the height: - Height = side * sin(angle)

Using the given side length of 12 units, we can calculate the height as follows:

- Height = 12 * sin(30 * (π/180)) - Height = 12 * sin(π/6) - Height = 12 * 0.5 - Height = 6 units

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

- Area = (1/2) * base * height - Area = (1/2) * 12 * 6 - Area = 36 square units

Therefore, the area of the triangle is 36 square units.

Conclusion

The area of the triangle with one side measuring 12 units and adjacent angles of 30 and 75 degrees is 36 square units.