The Empire State Building in New York City is 1250 ft tall. What is the

distance from the top of this building to the horizon to the nearest mile? (Hint: 5280 ft 1 mi; radius of Earth 4000 mi)

The illustration forms a right angled triangle. The opposite side of the triangle is where we are looking for . The adjacent side is the radius 4000 miles.

5280 ft = 1 mile

735 ft = ? miles

cross multiply

735/5280

miles = 0.13920454545 miles

The hypotenuse side is the height of the building + 4000 miles = 0.140 + 4000 = 4000.14 miles

using Pythagoras theorem

c² = a² + b²

c = 4000.14

a = 4000

4000.14² = 4000² + b²

b² = 4000.14² - 4000²

b² = 16001120.0196 - 16000000

b² = 1120.0196

b = √1120.0196

b = 33.4666938911

b = 33 miles

The Empire State Building in New York City is 1250 ft tall. What is the distance from the top of this building to the horizon to the nearest mile? (Hint: 5280 ft 1 mi; radius of Earth 4000 mi)

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The Empire State Building in New York City is 1250 ft tall. What is the

distance from the top of this building to the horizon to the nearest mile? (Hint: 5280 ft 1 mi; radius of Earth 4000 mi)