I need to solve the rest of the triangle
A=126.5
a=17.2
c=13.5
Using the Law of Sines we get
a/sinA = c/sin C
17.2/sin126.5 = 13.5/sinc
I am confused on what to do next
solve for sinC. SinC=13.5(sin126.5deg)/17.2=.65
C= arcsin .65= 40.5 deg
B=180-A-C
then finally, use law of sines to find side b.
I understand the rest of the question. I am just having some problems understanding the first.
How did
17.2/sin126.5deg = 13.5/sin C
turn into
SinC=13.5(sin126.5deg)/17.2=.65
I get it now. You need to Cross-Multiply
To solve for angle C, you can rearrange the equation you wrote using the Law of Sines:
a/sinA = c/sinC
Cross-multiplying gives you:
a * sinC = c * sinA
Now, substitute the known values:
17.2 * sinC = 13.5 * sin126.5
To isolate sinC, divide both sides of the equation by 17.2:
sinC = (13.5 * sin126.5) / 17.2
Next, use a scientific calculator to evaluate sinC:
sinC ≈ 0.9308
Now, to find angle C, you can use the arcsin function, or sin^(-1), which is the inverse of the sine function. This will give you the measure of angle C.