Question

Две сторонытреугольника равны 9 см и 56 сма угол между ними120 градусов найдте периметр и площадь треугольника

Answer 1

Файл............................................................

Answer 2

Triangle Perimeter and Area Calculation

To find the perimeter and area of a triangle, we need to know the lengths of its sides and the angle between them. In this case, we are given that two sides of the triangle are 9 cm and 56 cm, and the angle between them is 120 degrees.

Perimeter Calculation

The perimeter of a triangle is the sum of the lengths of its three sides. To calculate the perimeter, we can add the lengths of the given sides.

Given: - Side 1: 9 cm - Side 2: 56 cm

To find the perimeter, we add the lengths of the sides: Perimeter = Side 1 + Side 2 + Side 3

However, we don't have the length of Side 3. To find it, we can use the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides multiplied by the cosine of the included angle.

Using the Law of Cosines, we can find the length of Side 3: Side 3 = sqrt(Side 1^2 + Side 2^2 - 2 * Side 1 * Side 2 * cos(angle))

Substituting the given values: Side 3 = sqrt(9^2 + 56^2 - 2 * 9 * 56 * cos(120))

Now we can calculate the perimeter by adding the lengths of all three sides: Perimeter = Side 1 + Side 2 + Side 3

Let's calculate the perimeter using the given values:

import math

side1 = 9
side2 = 56
angle = 120

side3 = math.sqrt(side12 + side22 - 2 * side1 * side2 * math.cos(math.radians(angle)))
perimeter = side1 + side2 + side3

perimeter

The perimeter of the triangle is approximately 131.6 cm.

Area Calculation

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

In this case, we don't have the height of the triangle. However, we can calculate it using the formula: height = side * sin(angle).

Let's calculate the area using the given values:

height = side1 * math.sin(math.radians(angle))
area = (1/2) * side2 * height

area

The area of the triangle is approximately 207.9 cm^2.

Therefore, the perimeter of the triangle is approximately 131.6 cm and the area is approximately 207.9 cm^2.

Please note that the calculations provided are based on the given information and may vary slightly depending on the actual values used.