The side of the triangle is 28 cm, and the other two form an angle of 60 degrees.

| April 29, 2021 | education

The side of the triangle is 28 cm, and the other two form an angle of 60 degrees. Their difference is 20 cm. Find the sides of the triangle.

Let the AC side be equal to X cm, then, by condition, the AB side = (X + 20) cm.

Let us use to solve the cosine theorem for.

BC ^ 2 = AC ^ 2 + AB ^ 2 – 2 * AC * AB * CosA.

28 ^ 2 = X ^ 2 + (X + 20) ^ 2 – 2 * X * (X + 20) * Cos60.

784 = X ^ 2 + X ^ 2 + 40 * X + 400 – (2 * X ^ 2 + 40 * X) * 1/2.

X ^ 2 + 20 * X – 384 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 20 ^ 2 – 4 * 1 * (-384) = 400 + 1536 = 1936.

X1 = (-20 – √1936) / (2 * 1) = (-20 – 44) / 2 = -64/2 = -32. (Doesn’t fit because <0).

X2 = (-20 + √1936) / (2 * 1) = (-20 + 44) / 2 = 24/2 = 12 cm.

Side AC = 12 cm, then AB = (12 + 20) = 32 cm.

Answer: The sides of the triangle are 12 and 32 cm.



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