Given with a = 12, b = 6, and mA 50° , find mC . Round the sine value to the nearest thousandth and answer to the nearest whole degree.
Direct and simple application of the Sine Law.
Give me your starting equation
That is the way our teacher gave us the problem. I do not really understand this
If your teacher gave you this problem the way it is, then it is a simple
application of the sine law.
You must have been given that, or you must have studied it, or else
this question cannot be done.
I suggest you find angle B first, then by the sum of the angles of a
triangle theorem you can find C
To find mC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant. In this case, we know that the length of side a is 12 and the measure of angle mA is 50°.
So, we can use the Law of Sines equation:
sin(mA) / a = sin(mC) / c
We can substitute the known values into the equation:
sin(50°) / 12 = sin(mC) / c
Now, we can find the value of sin(mC) by rearranging the equation and solving for sin(mC):
sin(mC) = (sin(50°) / 12) * c
To find the value of c, we can use the Law of Cosines, which states that in any triangle, the square of the length of one side is equal to the sum of the squares of the other two sides, minus twice the product of the two sides and the cosine of the included angle.
The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(mC)
We can substitute the known values into the equation:
c^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(mC)
Simplifying the equation:
c^2 = 144 + 36 - 144 * cos(mC)
c^2 = 180 - 144 * cos(mC)
To find the value of c, we need to find the value of cos(mC). Rearrange the equation and solve for cos(mC):
cos(mC) = (180 - c^2) / (144)
Now that we have the sine and cosine of mC, we can solve for mC:
sin(mC) = (sin(50°) / 12) * c
cos(mC) = (180 - c^2) / (144)
To find the value of mC, use the inverse sine function (sin^(-1)) to find the angle in radians first, then convert it to degrees:
mC = sin^(-1)([(sin(50°) / 12) * c]) in radians
Finally, round the sine value to the nearest thousandth and the answer to the nearest whole degree to get the value of mC.