Question

Use the Law of Sines to solve the triangle. Round your answers to two decimal places.A = 8° 40', B = 13° 15', b = 4.8

Answer 1

Given

`A=8°40^(\prime),B=13°15^(\prime),b=4.8`

To find the value of a, c, C.

Step-by-step explanation:

It is given that,

`A=8°40^(\prime),B=13°15^(\prime),b=4.8`

Since,

`A=8°40^(\prime),B=13°15^(\prime)`

Then,

`\begin{gathered} A+B+C=180 \\ 8\degree40^(\prime)+13\degree15^(\prime)+C=180\degree \\ C=180\degree-21\degree55^(\prime) \\ C=(179-21)\degree(60^-55^)^(\prime) \\ C=158\degree5^(\prime) \end{gathered}`

Therefore, by using Sine law,

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c) \\ (\sin8\degree40^(\prime))/(a)=(\sin13\degree15^(\prime))/(4.8)=(\sin158\degree5^(\prime))/(c) \\ \Rightarrow(\sin8\degree40^(\prime))/(a)=(\sin13\degree15^(\prime))/(4.8) \\ \Rightarrow(\sin13\degree15^(\prime))/(4.8)=(\sin158\degree5^(\prime))/(c) \end{gathered}`

Therefore,

`\begin{gathered} \begin{equation*} (\sin8\degree40^(\prime))/(a)=(\sin13\degree15^(\prime))/(4.8) \end{equation*} \\ (0.14608)/(a)=(0.227501)/(4.8) \\ a=(0.14608)/(0.047396) \\ a=3.08211 \\ a=3.1 \end{gathered}`

Also,

`\begin{gathered} \begin{equation*} (\sin13\degree15^(\prime))/(4.8)=(\sin158\degree5^(\prime))/(c) \end{equation*} \\ 0.047396=(0.366501)/(c) \\ c=(0.366501)/(0.047396) \\ c=7.73274 \\ c=7.7 \end{gathered}`

Hence, the answer is

`C=158\degree5^(\prime),a=3.1,c=7.7`