In triangle ABC, if angle A = 60 degrees, angle B = 70 degrees, and side a = 10

In triangle ABC, if angle A = 60 degrees, angle B = 70 degrees, and side a = 10 cm, what is the length of side b using the Law of Sines?

In triangle ABC, if angle A = 60 degrees, angle B = 70 degrees, and side a = 10 cm, what is the length of side b using the Law of Sines?

Step 1: Identify the given information. We have angle A = 60 degrees, angle B = 70 degrees, and side a = 10 cm.
Step 2: Use the Law of Sines formula, which states that a/sin(A) = b/sin(B).
Step 3: Rearrange the formula to solve for side b: b = a * (sin(B)/sin(A)).
Step 4: Substitute the known values into the formula: b = 10 * (sin(70)/sin(60)).
Step 5: Calculate sin(70) and sin(60). Use a calculator to find that sin(70) ≈ 0.9397 and sin(60) ≈ 0.8660.
Step 6: Substitute these values back into the equation: b = 10 * (0.9397/0.8660).
Step 7: Perform the division: 0.9397 / 0.8660 ≈ 1.084.
Step 8: Multiply by 10 to find b: b ≈ 10 * 1.084 ≈ 10.84 cm.
Step 9: Round the answer if necessary. The length of side b is approximately 10.80 cm.

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