Question

Find the number that belongsin the green box.141570° [?]

Answer 1

From the diagram, we are to find the value of x.

Using the sine rule

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B) \\ \text{where a=15. A=70}^0,b=14,B=x^0 \end{gathered}`
`\begin{gathered} (15)/(\sin70)=(14)/(\sin x) \\ by\text{ cross multiplication, we have } \\ 15\sin x=14\sin 70 \end{gathered}`
`\begin{gathered} we\text{ now divide both side by 15} \\ \sin x=(14\sin 70)/(15) \\ \sin x=(14(0.9397))/(15) \\ \sin x=(13.1557)/(15) \\ \sin x=0.8770 \end{gathered}`

To find the angle x, you take the sin inverse of the value of the right-hand side

`\begin{gathered} x=\sin ^(-1)(0.8770) \\ x=61.28^0 \end{gathered}`

Hence the number that belongs to the green box is 61.3 to the nearest tenth