Question

I took this today and just want to know how to do it next time I get a problem like this

Answer 1

In the given figure,

In triangle DEF,

`\tan 45^(\circ)=(12)/(EF)\Rightarrow EF=12`
`\sin 45^(\circ)=(12)/(DF)\Rightarrow\frac{1}{\sqrt[]{2}}=(12)/(DF)=DF=12\sqrt[]{2}`

The length of DF is

`12\sqrt[]{2}`

Now in triangle DFG,

`\tan 45^(\circ)=(DF)/(FG)=\frac{12\sqrt[]{2}}{FG}`
`FG=12\sqrt[]{2}`

The length of FG is

`12\sqrt[]{2}`

Now apply Pythagoras theorem to determine DG,

`DG^2=(12\sqrt[]{2})^2+(12\sqrt[]{2})^2`
`DG^2=288+288=576`
`DG=\sqrt[]{576}=24`

The length of DG is 24.