The two sides of the triangle are 9 cm and the angle 56 cm between them is 120 degrees, find the perimeter and area of the triangle.
The area of a triangle can be determined by the formula S = a * b * sin (a ^ b), where a and b are two sides of the triangle, sin (a ^ b) is the sine of the angle between them.
S = 9 * 56 * sin120 = 9 * 56 * √3 / 2 = 252√3 cm2.
By the cosine theorem, the square of the side of a triangle is equal to the sum of the squares of the other two sides minus the double product of these sides by the cosine of the angle between them: c ^ 2 = a ^ 2 + b ^ 2-2 * a * b * cos (a ^ b).
c ^ 2 = 9 ^ 2 + 56 ^ 2-2 * 9 * 56 * cos120 = 81 + 3136-1008 * (- 0.5) = 81 + 3136 + 504 = 3721;
c = √3721 = 61 cm.
Perimeter of a triangle:
P = a + b + c = 9 + 56 + 61 = 126 cm.
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