Question

stephan, who is twice as tall as his younger brother nik is 6.7 feet tall. they are standing on opposite sides of a mirror, far enough away so only thier heads show in the reflection. if nik is standing 23.5 feet away from the mirror, how far away is stephan standing? round your answer to the nearest hundredths. 560 inches

Explanation:

Step1: Set up the proportion

Since the triangles formed by their heights and distances from the mirror are similar. Let \(x\) be the distance of Stephan from the mirror. The ratio of their heights is equal to the ratio of their distances from the mirror. Stephan's height \(h_S = 6.7\) feet, Nik's height \(h_N=\frac{6.7}{2}\) feet. Let Nik's distance from the mirror be \(d_N = 23.5\) feet. The proportion is \(\frac{h_S}{h_N}=\frac{x}{d_N}\).

Step2: Substitute the values

Substitute \(h_S = 6.7\), \(h_N=\frac{6.7}{2}\), and \(d_N = 23.5\) into the proportion \(\frac{6.7}{\frac{6.7}{2}}=\frac{x}{23.5}\). Simplify the left - hand side: \(\frac{6.7}{\frac{6.7}{2}}=2\). So the equation becomes \(2=\frac{x}{23.5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(2=\frac{x}{23.5}\) by \(23.5\). We get \(x = 2\times23.5=47.00\) feet.

Answer:

\(47.00\) feet