Question

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. (Let b = 5.1.)

Answer 1

Given:-

An image with triangle.

To find:-

The value of B,a,c.

So the laws of sines are,

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

So now we substitute the known values. we get,

`(\sin16)/(a)=(\sin B)/(5.1)=(\sin125)/(c)`

Now we find the value of B,

Since the sum of angles of the triangle is 180. we get,

`\begin{gathered} A+B+C=180 \\ 16+B+125=180 \\ B+141=180 \\ B=180-141 \\ B=39 \end{gathered}`

So substituting the value we get,

`(\sin16)/(a)=(\sin 39)/(5.1)=(\sin125)/(c)`

Now we find the value of a. we get,

`\begin{gathered} (\sin16)/(a)=(\sin 39)/(5.1) \\ (0.2756)/(a)=(0.6293)/(5.1) \\ a=(0.2756*5.1)/(0.6293) \\ a=2.2335 \end{gathered}`

Now we find c. we get,

`(0.2756)/(2.2335)=(\sin 125)/(c)`

So