Question

A satellite, B, is 17,000 miles from the horizon of Earth. Earth's radius is about 4,000 miles. Find the approximate distance the satellite is from the Earth's surface. The diagram is not to scale.

Answer 1

Answer:

• 13,464 miles

Explanation:

1) You can draw a right triangle where the distance of 17,000 miles from the horizon of Earth is leg, perpendicularto the radius of the Earth, and such radius is the other leg, 4,000 miles.

2) By the construction of the right triangle, the hypotenuse is the sum of the height of the satelite (unknown, x) plus the radius of the Earth (4,000) = x + 4,000.

3) Now, you can use Pythagora's theorem:

• (x+4,000)² = 4,000² + 17,000²

• (x + 4,000)² = 305,000,000

• (x + 4,000) = 17,464       (take only the positive root)

• x = 17,464 - 4000 = 13,464

Remember to include the units: miles.

Answer: 13,464 miles. 

Answer 2

Answer: The approximate distance between the earth and the satellite is 13464.24 miles

Step-by-step explanation:

Since we have given that

Distance of a satellite from the horizon of Earth = 17000 miles

Radius of earth = 4000 miles

As shown in the figure below:

Let the distance between the earth and the satellite be 'x'.

So, AO = OB = 4000 miles (Radii of the circle)

BC = 'x' units

AC= 17000 miles

As we know that the tangent from the external point forms right angle with the radius of the circle.

So, In Δ ABC,

$OC^2=AC^2+OA^2\\\\(x+4000)^2=17000^2+4000^2\\\\x+4000=\sqrt{289000000+16000000}\\\\x+4000=17464.24( \text{ we ignore the negative term as distance can't be in negative})\\\\x=17464.24-4000\\\\x=13464.24$

Hence, the approximate distance between the earth and the satellite is 13464.24 miles.