Elevation of the road at 5 miles from the starting point is 1250 ft.
Similarity of triangles:
- If two triangles are similar, their corresponding sides will be proportional.
Given in the question,
Two triangles formed by a road are ΔADE and ΔABC (As shown in the figure attached).
Since, ∠A ≅ ∠A (Reflexive property)
∠AED ≅ ∠ACB (right angles)
ΔADE ~ ΔABC (By A-A property of similarity)
In these similar triangles, corresponding sides will be proportional.
[tex]\frac{AB}{BC}=\frac{AD}{DE}[/tex]
[tex]\frac{8}{2000}=\frac{5}{DE}[/tex]
[tex]DE=\frac{5\times 2000}{8}[/tex]
[tex]=1250[/tex] miles
Therefore, elevation of the road at 5 miles from the starting point will be 1250 ft.
Option (B) will be the answer.
Learn more about the similarity of the triangles here,
https://brainly.com/question/20826545?referrer=searchResults
