In triangle ABC AB = 8 cm, BC = 5 cm, AC = 7 cm.Find the cosine of angle C and the area of triangle ABC.
| August 9, 2021 | education
To determine the magnitude of the cosine of an angle, we apply the cosine theorem for a triangle.
AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * CosACB.
64 = 49 + 25 – 2 * 7 * 5 * CosACB.
70 * CosACB = 10.
CosACB = 10/70 = 1/7.
The area of the triangle is determined by Heron’s theorem.
We calculate the half-perimeter of the triangle: p = (AB + BC + AC) / 2 = (8 + 5 + 7) / 2 = 10 cm.
Sav = √10 * (10 – 8) * (10 – 5) * (10 – 7) = √10 * 2 * 5 * 3 = √300 = 10 * √3 cm2.
Answer: The area of the triangle is 10 * √3 cm2, the cosine of the angle ACB is 1/7.
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