The diagram shows two campsites on opposite ends of a lake and two triangles formed by intersecting segments from the campsites.
Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not drawn to scale. The triangles are proportional.
To find the distance between campsites F and G, we need to use a proportional relationship between the two triangles.
Let's call the distance between campsite F and the point where the segments intersect X, and the distance between campsite G and the point where the segments intersect Y.
In triangle FDE, we have the proportions:
EF/DE = X/50
In triangle GDF, we have the proportions:
DG/DF = Y/30
From the given measurements in the diagram, we have:
EF = 70, DE = 50, DG = 90, DF = 30
Using these proportions, we can solve for X and Y:
EF/DE = X/50
70/50 = X/50
X = 70
DG/DF = Y/30
90/30 = Y/30
Y = 90
Therefore, the distance between campsites F and G is X + Y which is:
70 + 90 = 160
So, the distance between the two campsites is 160 units.