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.

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 SB60m class=

Respuesta :

Answer:

AB=[tex]75m[/tex]

Step-by-step explanation:

In the [tex]\Delta SCB[/tex] and [tex]\Delta SDA[/tex]

[tex]\angle S=\angle S\\BC||AD\\\Rightarrow\angle SBC=\angle SAD\\\angle SCB =\angle SDA[/tex]

[tex]By\ AAA\ \Delta\ and\ \Delta SDA\ are\ similar\\\\ \Rightarrow\frac{SC}{SD} =\frac{SB}{SA} \\\\ \frac{80}{180} =\frac{60}{SA}\\\\ SA=60\times\frac{180}{80} \\\\SA=135\\\\AB=SA-SB\\\\=135-60\\\\=75m[/tex]