Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).7, sine, B, minus, square root of, 30, end square root, equals, 07sinB− 30 =0
Question
Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).7, sine, B, minus, square root of, 30, end square root, equals, 07sinB− 30 =0
Solution
The given equation is 7sinB - √30 = 0.
Step 1: Isolate sinB by adding √30 to both sides of the equation and then dividing by 7.
7sinB = √30 sinB = √30 / 7
Step 2: Use the inverse sine function to find the value of B.
B = sin^(-1)(√30 / 7)
Step 3: Use a calculator to find the approximate value of B.
B ≈ 38.2 degrees
Step 4: Since the sine function has a period of 360 degrees and is positive in both the first and second quadrants, there is another solution in the second quadrant.
B2 = 180 - 38.2 = 141.8 degrees
So, the solutions to the equation 7sinB - √30 = 0 in the interval 0 ≤ B < 360 are B ≈ 38.2 degrees and B ≈ 141.8 degrees.
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