Question

QuestionIn ABC, we are told that b = 7, LA = 44°, and ZC = 60°, Solve for a and c,

Answer 1

Since interior angles of any triangle add up to 180, we have

`\angle B+60+44=180`

which gives

`\begin{gathered} \angle B+104=180 \\ \text{then} \\ \angle B=180-104 \\ \angle B=76 \end{gathered}`

Now, in order to find c, we can apply the law of sines, that is,

`\begin{gathered} (\sin C)/(c)=(\sin B)/(b) \\ \text{that is,} \\ (\sin60)/(c)=(\sin76)/(7) \end{gathered}`

or equivalently,

`(c)/(\sin60)=(7)/(\sin 76)`

Then, by moving sin60 to the right hand side, we get

`c=\sin 60*(7)/(\sin 76)`

which gives

`\begin{gathered} c=0.8660*(7)/(0.97029) \\ c=6.24757 \end{gathered}`

Similarly, by the law of sines, we have

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b) \\ \text{that is,} \\ (\sin 44)/(a)=(\sin 76)/(7) \end{gathered}`

or equivalently,

`(a)/(\sin44)=(7)/(\sin 76)`

then, a is given as

`\begin{gathered} a=\sin 44*(7)/(\sin 76) \\ a=0.6946*(7)/(0.97029) \\ a=5.011 \end{gathered}`

In summary, the answers are