Question

Find the value of x. Round tothe nearest tenth.27°X34°11X == [?]Law of Sines: sin Asin Bb=sin CaС

Answer 1

In the given triangle ABC,

Using sine rule

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

Therefore,

`\begin{gathered} (\sin27)/(11)\text{ = }(\sin34)/(x)=(\sin B)/(c) \\ (\sin27)/(11)\text{ = }(\sin34)/(x) \end{gathered}`

Cross multiplying on both the sides,

`\begin{gathered} \sin \text{ 27 }*\text{ x = sin34 }*\text{ 11} \\ x\text{ = }\frac{\text{sin34 }*\text{ 11}}{\sin\text{ 27}} \\ x\text{ = 13.549} \\ x\text{ }\approx13.55 \end{gathered}`

Thus the value of x is 13.55 .