Question

I need help with this question it's to find the distance.

Answer 1

45'

Step-by-step explanation

Let the distance across the swamp be S.

The two triangles in the figure are similar triangles.

This means that the ratio of corresponding sides of the triangles are equal.

That is:

`(20)/(80)=(S)/(100+80)`

Solving for S:

`\begin{gathered} (20)/(80)=(S)/(180) \\ \text{Cross}-mu\text{ltiply:} \\ 20\cdot180=S\cdot80 \\ 3600=S\cdot80 \\ \text{Divide both sides by 80:} \\ S=(3600)/(80) \\ S=45^(\prime) \end{gathered}`

Therefore, the distance across the swamp is 45'.