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?
Practice Questions
1 question
Q1
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?
8.66 cm
10 cm
12.25 cm
15 cm
Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.
Steps: 10
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)).
