Find all the solutions of the following triangle using the Law of Sines.

Angle A: 83°20'
Angle C: 54.6°
c: 18.1

How would I find I find angle B? I know that you would subtract angle A and C from 180, but I do not understand how to maintain the minutes (') on my calculator.

You could always punch in

1/3 + 83 sin

to get sin of 83 1/3 degrees.

Or, just get sin 83.333333333 degrees. It should be close enough.

So, assuming you can in fact evaluate your sines, just use the fact that

A+B+C = 180°
so, B = 180° - 83°20' - 54°36' = 42°4' = 42 1/15 ° = 42.06666666°

b/sinB = c/sinC
b = csinB/sinC = 18.1(.67)/.815 = 14.88

To find angle B in the given triangle, you can use the Law of Sines, which states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In other words, in a triangle ABC with sides a, b, c opposite to angles A, B, C respectively, the Law of Sines can be expressed as:

sin(A)/a = sin(B)/b = sin(C)/c

To find angle B, you can rearrange the formula as follows:

sin(B) = (sin(A) * b) / a

Now, let's calculate it step by step:

1. Convert the angle measurements to decimal form:
Angle A: 83°20' = 83 + 20/60 = 83.3333°
Angle C: 54.6°

2. Substitute the given values into the Law of Sines:
sin(B) = (sin(83.3333°) * b) / 18.1

3. Calculate sin(B) using your calculator:
Enter sin(83.3333°), then multiply it by b, and finally divide by 18.1.

Note: Most scientific calculators have a function to input degrees, minutes, and seconds. If your calculator does not have such a function, you can convert the minutes to degrees by dividing them by 60 and adding the result to the whole number degrees.

4. Once you have calculated sin(B), use the inverse sine function (sin^(-1)) to find the value of angle B:
B = sin^(-1)(calculated sin(B))

Make sure to perform every step accurately to get the correct value of angle B.