Question

A satellite at point b is 4,800 miles from point a on earth. Earth radius is about 4,000 miles. segment AB is tangent to the circle.

What is the approximate distance between the satellite and earths surface ?
a.8,800 miles b.6,248 miles c. 2,248 miles d. 800 miles

Answer 1

We are given the following:
AB = 4800 miles
AO = 4000 miles
There is also a rule that states that a line tangent to a circle, will be perpendicular to the radius of the circle at the point of tangency. Therefore, triangle BAO is a right triangle.

We use Pythagorean theorem to solve for the hypotenuse BO.
BO = √(AO²+AB²) = √(4000²+4800²) = 6248 miles

But the problem asks for the length of BC. Since we know that OC is a radius of the circle, then:
BC = 6248 - 4000 = 2,248 miles.

The answer is C.