Question

1. to find the width of a river, jordan surveys the area and finds the following measures. find the width of the river. 34.2 m 79.6 m 18.6 m

Explanation:

Step1: Identify similar triangles

The two right triangles are similar (by AA similarity, as both have a right angle and share the angle formed by the diagonal). Let the width of the river be \( x \) (the height of the larger right triangle). The smaller triangle has height \( 18.6 \) m and base \( 34.2 \) m, the larger triangle has height \( x \) and base \( 79.6 \) m.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{x}{79.6}=\frac{18.6}{34.2}\)

Step3: Solve for \( x \)

Cross - multiply: \( x=\frac{18.6\times79.6}{34.2}\)

First, calculate \( 18.6\times79.6 = 18.6\times(80 - 0.4)=18.6\times80-18.6\times0.4 = 1488-7.44 = 1480.56\)

Then, divide by \( 34.2 \): \( x=\frac{1480.56}{34.2}\approx43.3\) (rounded to one decimal place)

Answer:

The width of the river is approximately \( 43.3 \) meters.