Question

I am currently stuck on question number 5. Can you please help me?

Answer 1

Step 1

Find the missing angle taken as y

`\begin{gathered} y+28+126=180\text{ (sum of angles in a triangle)} \\ y=180-28-126 \\ y=26^(\circ) \end{gathered}`

Step 2

State sine rule

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

where;

`\begin{gathered} a=8.2 \\ A=26^(\circ) \\ b=x \\ B=28^(\circ) \end{gathered}`

Step 3

Substitute and find the value of x

`\begin{gathered} (\sin26)/(8.2)=(\sin28)/(x) \\ x\sin 26=8.2\sin 28 \\ (x\sin26)/(\sin26)=(8.2\sin28)/(\sin26) \\ x=8.781752273 \\ x\approx8.8\text{ to the nearest tenth} \end{gathered}`

Hence, x= 8.8 to the nearest tenth. Option C