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In triangle ABC, angle A measures 60 degrees and angle B measures 45 degrees. The length of side AC is 10 units. Find the length of side BC.

answer

To find the length of side BC, we can use the Law of Sines. According to the Law of Sines, the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle. Let's denote the length of side BC as x. Using the Law of Sines, we have: sin(A) / BC = sin(B) / AC Substituting the given values, we get: sin(60) / x = sin(45) / 10 Simplifying further: √3 / x = √2 / 10 Cross-multiplying: √3 * 10 = √2 * x Simplifying: 10√3 = √2x Squaring both sides: 300 = 2x^2 Dividing by 2: 150 = x^2 Taking the square root: x = √150 Simplifying: x ≈ 12.25 Therefore, the length of side BC is approximately 12.25 units.

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