What is a positive value of A in the interval [ 0 ° , 90 ° ) \left[0\degree,90\degree\right) [ 0° , 90° ) that will make the following statement true? Express the answer in four decimal places. sin ⁡ A = 0.9235 \sin A=0.9235 sin A = 0.9235

Let's give this problem a try. So here it says, what is a positive value of a in the interval from 0 to 90 degrees that will make the following statement true, and we need to express our answer in 4 decimal places. Okay. So to solve this problem, all we really need to do is isolate a by itself. And we can do this by taking the inverse sign on both sides of this equation. This will get the inverse sign and the sign to cancel, leaving us with just a, which is what we're looking for. So a is going to equal the inverse sign of 0.9235. And if you go ahead and take this and plug it in your calculator, what you want to do is make sure your calculator is in degree mode. And we talked about how you can check this by pressing the mode button on your calculator, and you will should see a menu that says degree or radian. Make sure you are in degree mode. And the reason we want to be in degree mode is because notice our interval is from 0 to 90 degrees. So that's a good sign that we need to use degree mode. So if you go ahead and plug this number into your calculator, the value that you should get is approximately 67 point 44324384, and then this keeps going on. But because we're asked to express our answer in 4 decimal places, looking at our decimal place, we need to go 1, 2, 3, 4 places to the right of the decimal point, which will give us that a is equal to 67.4 432 rounded to 4 decimal places. And that right there is the answer to the problem.