Question

1. connecting to real life you take a water sample to test for chloride. the sample must be taken from water at least 20 feet deep. find the depth of the water 50 feet from shore. is this an appropriate location for a water sample?

Explanation:

Step1: Use similar triangles property

Since the two triangles (the large triangle representing the water - shore depth and the small triangle representing the sample - depth relation) are similar. For similar triangles, the ratios of corresponding sides are equal. Let the depth of the sample be \(h = 1.5\) ft, the total depth of water is \(H=5\) ft, the distance from shore for the large - scale is \(D = 50\) ft, and the distance from shore for the sample is \(d\). The ratio is \(\frac{h}{H}=\frac{d}{D}\).

Step2: Substitute the values

We know \(h = 1.5\), \(H = 5\), and \(D=50\). Substituting into \(\frac{h}{H}=\frac{d}{D}\), we get \(\frac{1.5}{5}=\frac{d}{50}\).

Step3: Solve for \(d\)

Cross - multiply: \(5d=1.5\times50\). Then \(5d = 75\). Divide both sides by 5: \(d=\frac{75}{5}=15\) ft. Since \(15\lt20\), this is not an appropriate location.

Answer:

The distance from shore \(d = 15\) ft. No, this is not an appropriate location.