Question

1. paul is taking a picture next to big tex at the texas state fair. he wants to know how tall big tex is, so he measures the length of his shadow and the shadow cast by the statue. the measurements are shown in the picture.

choose the correct answer from the dropdown to complete the sentence.
big tex is feet tall.

Explanation:

Step1: Set up the proportion

Since the triangles formed by Paul, his shadow and Big Tex, its shadow are similar (by the AA similarity criterion as the angles of elevation of the sun are the same), we can set up the proportion \(\frac{\text{Paul's height}}{\text{Paul's shadow length}}=\frac{\text{Big Tex's height}}{\text{Big Tex's shadow length}}\). Let \(h\) be the height of Big Tex. We know Paul's height is \(5\) ft, Paul's shadow length is \(1.25\) ft and Big Tex's shadow length is \(13.75\) ft. So the proportion is \(\frac{5}{1.25}=\frac{h}{13.75}\).

Step2: Solve the proportion for \(h\)

Cross - multiply the proportion: \(1.25h = 5\times13.75\). First, calculate \(5\times13.75=68.75\). Then, solve for \(h\) by dividing both sides of the equation \(1.25h = 68.75\) by \(1.25\). So \(h=\frac{68.75}{1.25}\).

Step3: Perform the division

\(h = 55\) (since \(68.75\div1.25=\frac{6875}{125}=55\)).

Answer:

\(55\)