Question

Find the distance between points A and B, located on the opposite shores of a river, if on one of the shores following segments have been drawn and measured SB=60m, SC=80m, SD=180m and BC∥AD.

Answer 1

AB=
`75m`

Explanation:

In the
`\Delta SCB` and
`\Delta SDA`

`\angle S=\angle S\\BC||AD\\\Rightarrow\angle SBC=\angle SAD\\\angle SCB =\angle SDA`

`By\ AAA\ \Delta\ and\ \Delta SDA\ are\ similar\\\\ \Rightarrow(SC)/(SD) =(SB)/(SA) \\\\ (80)/(180) =(60)/(SA)\\\\ SA=60*(180)/(80) \\\\SA=135\\\\AB=SA-SB\\\\=135-60\\\\=75m`