Question

Две стороны треугольника равны 3 сантиметров и 5 сантиметров а угол между ними равен 30 градусов найдите третью сторону и площадь треугольника можно прямо сейчас только решение

Answer 1

Сторона=v(3^2+5^2-2*3*5*cos30)=v(9+25-30*v3/2)=v(34-15v3) см  упс...какой кривой ответ получился
площадь=1/2*3*5*sin30=3*5/4=15/4=3,75 см.кв.

Answer 2

Given Information:

We are given that two sides of a triangle are 3 centimeters and 5 centimeters, and the angle between them is 30 degrees.

Finding the Third Side:

To find the length of the third side of the triangle, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we have: a = 3 centimeters b = 5 centimeters C = 30 degrees

Substituting these values into the equation, we can solve for c:

c^2 = 3^2 + 5^2 - 2 * 3 * 5 * cos(30)

Simplifying the equation:

c^2 = 9 + 25 - 30 * cos(30)

Using a calculator to evaluate cos(30) ≈ 0.866, we get:

c^2 = 9 + 25 - 30 * 0.866

c^2 ≈ 9 + 25 - 25.98

c^2 ≈ 8.02

Taking the square root of both sides, we find:

c ≈ √8.02

c ≈ 2.83 centimeters

Therefore, the length of the third side of the triangle is approximately 2.83 centimeters.

Finding the Area of the Triangle:

To find the area of the triangle, we can use the formula for the area of a triangle given two sides and the included angle:

Area = (1/2) * a * b * sin(C)

In our case, we have: a = 3 centimeters b = 5 centimeters C = 30 degrees

Substituting these values into the formula, we can calculate the area:

Area = (1/2) * 3 * 5 * sin(30)

Using a calculator to evaluate sin(30) ≈ 0.5, we get:

Area = (1/2) * 3 * 5 * 0.5

Area = 7.5 * 0.5

Area = 3.75 square centimeters

Therefore, the area of the triangle is 3.75 square centimeters.

Conclusion:

The length of the third side of the triangle is approximately 2.83 centimeters, and the area of the triangle is 3.75 square centimeters.