Question

Three moons are in the same circular orbit around a planet. The moons are each 115,000 kilometers from the surface of the planet, located at points A, B, and C. The planet is 45,000 kilometers in diameter and m∠ABC=90∘. How far is point A from point C?

Answer 1

Answer:

275,000

Step-by-step explanation:

Diametre of the planet = 45,000

Each moon is 115,000 away from the planet (represented by A, B, and C

Moons A, B, and C form a right triangle.

AC form the hypotenuse.

So, take the distance from the Planet to moon C (115,000) add it the distance from the Planet to Moon A (115,000) and add the diametre of the planet (45,000) to get the answer 275,000

2(115,000) + 45,000 = 275,000

Answer 2

The distance between points A and C is 275000 kilometers.

According to the information given on statement and the reconstruction given by the figure, we conclude that distance between points A and C ($x$), in kilometers is:

$x = D + 2\cdot h$ (1)

Where:

• $D$ - Diameter of the planet, in kilometers.
• $h$ - Distance from the surface of the planet and each moon, in kilometers.

If we know that $D = 45000\,km$ and $h = 115000\,km$, then the distance between points A and C is:

$x = 45000\,km + 2\cdot (115000\,km)$

$x = 275000\,km$

The distance between points A and C is 275000 kilometers.

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