In ABC, sin A equals 2/3 , sin B equals 4/5 , and side a equals 20 Find side b?
To find side b of triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
The formula for the Law of Sines is as follows:
a/sin(A) = b/sin(B) = c/sin(C)
Given that sin A is 2/3, sin B is 4/5, and side a is 20, we can substitute the values into the formula:
20/sin(A) = b/sin(B)
Let's solve it step by step:
Step 1: Substitute the given values
20/(2/3) = b/(4/5)
Step 2: Simplify
20 * (3/2) = b * (5/4)
Step 3: Multiply
30 = 5/4 * b
Step 4: Divide both sides by 5/4
b = 30 / (5/4)
Step 5: Divide fractions
b = 30 * (4/5)
Step 6: Multiply
b = 24
Therefore, side b of triangle ABC is equal to 24.