Question

on your trip to arches national park, you decide to hike to delicate arch. while you are standing at the base of the arch, you notice that your shadow is 33 feet long, while the shadow of the arch is 115 feet long. if you are 5.2 feet tall, how tall is delicate arch? round your answer to the nearest hundredths.
en su viaje al parque nacional arches, decide caminar hasta delicate arch. mientras estás parado en la base del arco, notas que tu sombra mide 33 pies de largo, mientras que la sombra del arco mide 115 pies de largo. si mide 5.2 pies de altura, ¿qué altura tiene delicate arch? redondea tu respuesta a las centésimas más cercanas.
feet

Explanation:

Step1: Set up the proportion

Since the height and shadow length are proportional, we have \(\frac{\text{Your height}}{\text{Your shadow length}}=\frac{\text{Arch height}}{\text{Arch shadow length}}\). Let \(h\) be the height of the arch. So \(\frac{5.2}{33}=\frac{h}{115}\).

Step2: Solve for \(h\)

Cross - multiply: \(33h = 5.2\times115\). First, calculate \(5.2\times115=598\). Then \(h=\frac{598}{33}\).

Step3: Calculate the value of \(h\)

\(h=\frac{598}{33}\approx18.12\) (rounded to the nearest hundredths).

Answer:

\(18.12\)