In a triangle ABC, the angle is C = 90 degrees. AC = 12, cosine of angle B = 0.6. Find the BC side.
| September 12, 2021 | education
1. Cosine ∠B = BC / AB.
BC / AB = 0.6.
BC = 0.6AB.
2. Calculate the length of the hypotenuse AB using the Pythagorean theorem:
AB² = AC² + BC².
AB² = 12² + (0.6AB) ² = 144 + 0.64AB²
0.36AB² = 144.
AB² = 144 / 0.36.
AB = √144 / 0.36 = 15 units.
3. Calculate the length of the BC leg using the Pythagorean theorem:
BC = √AB² – AC² = √15² – 12² = √225 – 144 = √81 = 9 units.
Answer: the length of the BC leg is 9 units.
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