Question

example #3: josh wanted to measure the height of the sears tower in chicago. he used a 12 - foot light pole and measured its shadow at 1 pm. the length of the shadow was 2 feet. then he measured the length of the sears towers shadow and it was 242 feet at that time. what is the height of the sears tower?

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the Sears Tower. Since the ratio of object height to shadow length is the same (similar triangles), we have \(\frac{\text{height of pole}}{\text{shadow of pole}}=\frac{\text{height of tower}}{\text{shadow of tower}}\), so \(\frac{12}{2}=\frac{h}{242}\).

Step2: Solve for \( h \)

Cross - multiply: \(2h = 12\times242\). Then \(h=\frac{12\times242}{2}\). Calculate \(12\times242 = 2904\), and \(\frac{2904}{2}=1452\).

Answer:

The height of the Sears Tower is \(1452\) feet.