Find the sine of the smaller angle of a triangle with sides 26 cm 28 cm 30 cm.
| February 24, 2021 | education
In the triangle opposite the smaller angle lies the smaller side of the triangle, then the sought angle ACB.
Let’s apply the cosine theorem for a triangle.
AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * CosACB.
676 = 784 + 900 – 2 * 28 * 30 * CosACB.
1680 * CosACB = 1008.
CosACB = 1008/1680 = 3/5 = 0.6.
Sin2ACB + Cos2ACB = 1.
Sin2ACB = 1 – Cos2ACB = 1 – 0.36 = 0.64.
SinACB = 0.8.
Answer: The sine of the smaller angle is 0.8.
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