Indirect Measurement – Width of a River
publish date: 2026/05/14 21:51:50.206928 UTC
A surveying crew needs to find the width of the river shown in the illustration below. Because of a dangerous current, they decide to stay on the west side of the river and use geometry to find its width. Their approach is to create two similar right triangles on dry land.Then they write and solve a proportion to find .
What is the width of the river?
Answer = (1) ft
Correct Answer
Explanation
To find the width \(w\), we set up a proportion comparing the "vertical" side of the river triangle to the "vertical" side of the land triangle, and the "diagonal" hypotenuse-segments of both.
The proportion is:
\[\frac{w}{20} = \frac{74}{25}\].
The Step-by-Step SolutionIsolate the variable \(w\) by multiplying both sides of the equation by 20:
\[w = \frac{74 \times 20}{25}\]
Calculate the numerator:
\[w = \frac{1480}{25}\]
Divide to find the final value:
\[w = 59.2\]
Final Result: The width of the river is 59.2 ft.
Reference
go-math-science.com