How tall is the arch if a boy is 5 feet tall and stands under the Gateway Arch in St Louis and casts a shadow that is 1 foot long and the shadow of the Arch is 126 feet long?

To find the height of the Gateway Arch, we can use the concept of similar triangles. The ratio of the boy's height to his shadow length is the same as the ratio of the Arch's height to its shadow length. Therefore, if the boy is 5 feet tall and casts a 1-foot shadow, the height of the Arch can be calculated as follows:

Height of Arch = (Height of boy / Length of boy's shadow) × Length of Arch's shadow = (5 feet / 1 foot) × 126 feet = 630 feet.

Thus, the Gateway Arch is 630 feet tall.