In triangle ABC AB = 5cm AC = 10cm angle BAC = 60 ° find BC.
| April 30, 2021 | education
To solve it, we use the formula of 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.
That is: BC ^ 2 = AC ^ 2 + AB ^ 2 – 2 * AC * AB * cos 60º.
Substitute the values and define the side of the aircraft.
BC^2 = 10 ^ 2 + 5 ^ 2 – 2 * 10 * 5 * cos 60º = 100 + 25 – 100 * cos 60º (cos 60º = 1/2) = 125 – 100 * 1/2 = 125 – 50 = 75.
BC^2 = 75.
BC = √75 = √ (25 * 3) = 5 * √3.
Answer: BC side = 5 * √3.
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