Question

A satellite is 19,000 miles from the horizon of Earth. Earth’s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth’s surface.

The diagram is not to scale.

Answer 1

The approximate distance is 15416 miles....

Explanation:

We have given:

A satellite is 19,000 miles from the horizon of earth.

The radius is 4,000 miles.

Lets say that BC =x

AO = OB = 4,000 miles

AC = 19,000 miles

The tangent from the external point forms right angle with the radius of the circle.

So in ΔABC

(OC)² = (AC)²+(OA)²

where OC = x+4000

AC = 19,000

OA = 4000

Therefore,

(x+4000)² = (19,000)² +(4,000)²

Take square root at both sides:

√(x+4000)² = √(19,000)² +(4,000)²

x+4000 =√361000000+16000000

x+4000 = √377000000

x+4000 = 19416.48

x= 19416.48 - 4000

x = 15416.48

Therefore the approximate distance is 15416 miles....