Question

the gateway arch in missouri casts a 140 foot shadow while a 18-foot pole casts a 4-foot shadow. how tall is the arch? a) 630 feet pajamas b) 654 feet bow-ties c) 672 feet gorilla costumes d) 688 feet tu-tus e) 705 feet sunglasses

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the Arch. The ratio of height to shadow length should be equal for the Arch and the pole. So, \(\frac{h}{140}=\frac{18}{4}\)

Step2: Solve for \( h \)

Cross - multiply: \( 4h = 18\times140 \)
Calculate \( 18\times140=2520 \)
Then \( h=\frac{2520}{4}=630 \)

Answer:

A) 630 feet