Question

A student visiting the Sears Tower Skydeck is 1353 feet above the ground. Find the distance the student can see to the horizon. Use the formula d=1.5h to approximate the distance d in miles to the horizon when h is the height of the viewer’s eyes above the ground in feet. Round to the nearest mile

Answer 1

The formula I used in Algebra 2 with my students involved those values, but you forgot the square root symbol. Distance to the horizon is actually
`d= √(1.5*h)`. This is because when you are standing up way higher than the ground and you are looking to the horizon far ahead and below you, your situation resembles a right triangle with your height as the leg of the right triangle, the distance out to how far you can see is the base of the triangle, and the hypotenuse is your line of sight far away and below you. The formula is derived from Pythagorean's Theorem. For us,
`d= √(1.5*1353)`. So d = 45.0 so 45 miles.