Question

Find the value of x. Round tothe nearest tenth.27°Х34°11=x = [?]Law of Sines: sin AAsin Bbsin CIIaС

Answer 1

Using the law of Sines

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

Consider the given triangle

Let A = 27°, the a = 11

Let B = 34°, the b = x

Substitute the values into the sine rule formula

This gives

`(\sin27)/(11)=(\sin 34)/(x)`

Cross multiply

`x*\sin 27=11*\sin 34`

Divide both sides by sin 27

This gives

`x=(11*\sin 34)/(\sin 27)`

Solve for x

`\begin{gathered} x=(11*0.5592)/(0.4540) \\ x=(6.1512)/(0.4540) \\ x=13.55 \end{gathered}`

Therefore, the value of x is approximately 13.55