Question

Campsite f and g are on opposite sides of the lake a survey crew made measurements on the diagram. What is the distance between the 2 campsites

Answer 1

Answer:

GF is 42.3 meters

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Verify if segment AB is parallel to segment FG

we know that

If segment AB is parallel to segment FG

then

Triangle ABO would be similar to Triangle GFO by AA Similarity theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

$\frac{AO}{GO}=\frac{BO}{FO}$

substitute the given values

$\frac{82}{73.8}=\frac{92}{82.8}$

Multiply in cross

$82(82.8)=92(73.8)\\6,789.6=6,789.6$

Is true

Therefore

Corresponding sides are proportional

segment AB is parallel to segment FG

Triangle ABO is similar to Triangle GFO by AA Similarity theorem

Find the distance between the two campsites FG

Applying proportion

$\frac{AO}{GO}=\frac{AB}{GF}$

substitute

$\frac{82}{73.8}=\frac{47}{GF}$

solve for GF

$GF=73.8(47)/82\\GF=42.3\ m$