In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?

Step 1: Identify the given values in triangle ABC. We have angle A = 45 degrees, side a = 10 cm, and angle B = 60 degrees.
Step 2: Use the Law of Sines formula, which states that a/sin(A) = b/sin(B).
Step 3: Rearrange the formula to find side b: b = a * (sin(B) / sin(A)).
Step 4: Substitute the known values into the formula: b = 10 * (sin(60) / sin(45)).
Step 5: Calculate sin(60) and sin(45). We know that sin(60) = √3/2 and sin(45) = √2/2.
Step 6: Substitute these values into the equation: b = 10 * ((√3/2) / (√2/2)).
Step 7: Simplify the fraction: (√3/2) / (√2/2) = (√3 / √2).
Step 8: Now, substitute back into the equation: b = 10 * (√3 / √2).
Step 9: Simplify further: b = 10 * √(3/2).
Step 10: Calculate the final value: b ≈ 8.66 cm.

No concepts available.