Solve for b 8.9sin(b)=5*sin(95)

Problem

8.9*sin(b)=5*sin(95)

Solution

1. Isolate the sine term by dividing both sides of the equation by 8.9

sin(b)=(5*sin(95))/8.9

2. Calculate the value of the right side of the equation using a calculator.

sin(b)≈(5*(0.99619))/8.9

sin(b)≈0.55966

3. Apply the inverse sine function to solve for b

b=arcsin(0.55966)

4. Determine the primary angle in degrees.

b≈34.03

5. Identify the second possible solution within the range [0,180] by subtracting the primary angle from 180

b=180−34.03

b≈145.97

Final Answer

b≈34.03,145.97

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