Question

The tallest building in Africa is the Carlton Centre in Johannesburg, South Africa. What is the distance from the top of this 735 ft building to the horizon to the nearest mile?

(Hint: 5,280 ft = 1 mi; radius of Earth = 4,000 mi)




The distance from the top of the building to the horizon is ______ miles

Answer 1

b = 33 miles

Explanation:

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