Question

1. in the figure, △abd is similar to △ecd. what is the height h of the drone when it is 8 feet from the cell phone tower?

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABD\sim\triangle ECD\), the ratios of their corresponding sides are equal. That is \(\frac{EC}{AB}=\frac{DE}{DA}\). Let \(EC = h\), \(AB=114\), \(DE = 32 - 8=24\), and \(DA = 32\). So we have the proportion \(\frac{h}{114}=\frac{24}{32}\).

Step2: Solve the proportion for \(h\)

Cross - multiply the proportion \(\frac{h}{114}=\frac{24}{32}\). We get \(32h=114\times24\). Then \(h=\frac{114\times24}{32}\). Simplify \(\frac{114\times24}{32}=\frac{114\times3}{4}\) (dividing numerator and denominator by 8). Now, \(114\times3 = 342\), and \(\frac{342}{4}=85.5\).

Answer:

\(h = 85.5\) feet