Question

In ∆MNO , o = 790cm. < O=50° and

Answer 1

Using the law of sines:

`\begin{gathered} (o)/(\sin(O))=(m)/(\sin (M)) \\ (790)/(\sin(50))=(m)/(\sin (25)) \\ m=(790\cdot\sin (25))/(\sin (50)) \\ m=435.834278 \end{gathered}`
`\begin{gathered} (o)/(\sin(O))=(n)/(\sin (N)) \\ (790)/(\sin(50))=(n)/(\sin (105)) \\ n=(790\cdot\sin (105))/(\sin (50)) \\ n=515.6358793 \end{gathered}`

Using the heron formula:

`\begin{gathered} s=(790+435.834278+515.6358793)/(2) \\ s=870.7350787 \\ so\colon \\ A=\sqrt[]{870.7350787(870.7350787-790)(870.7350787-435.834278)(870.7350787-515.6358793)} \\ \end{gathered}`
`\begin{gathered} A=104194.335 \\ A=104194cm^2 \end{gathered}`