A triangle has an angle whose sine is equal to 1/2. The angle is larger that 43 degrees in measure. Find the exact measure (in degrees) of the angle.
I did sin x = 1/2
and got 150 for the answer
Is this right?
Thank You!
Yes, your answer is correct!
To find the exact measure of the angle, we need to first find the reference angle. The reference angle is the acute angle between the terminal side of the angle and the x-axis in the standard position.
Since the sine of the angle is equal to 1/2, we know that the reference angle has a sine of 1/2 as well. Since the sine function is positive in the first and second quadrants, we can find the reference angle using the inverse sine function (also known as arcsine or sin^-1).
Using the inverse sine function, arcsin(1/2) gives us a reference angle of 30 degrees. However, we are looking for an angle larger than 43 degrees, so we need to add a revolution (360 degrees) to the reference angle. Therefore, the angle in question has a measure of 30 + 360 = 390 degrees.
So the exact measure (in degrees) of the angle is 390 degrees.
Well done on solving the problem!