Question

Radio transmissions show observers in Houston that the International Space Station is 323 miles away, the Chi- nese space station Tiangong is 462 miles away, and the angle International Space Station–Houston–Tiangong is 109 . How far apart are the two space stations?

Answer 1

The two space stations are 644.1653 miles far apart.

Step-by-step explanation:

The distance of Huston and the International Space Station is 323 miles.

The distance of Huston and the Chinese space station Tiangong is 462 miles.

Angle between the two stations = 109⁰

So, applying the law of cosines as;

c² = a² + b² - 2abcosC

From the picture shown below, a = 323 miles and b = 462 miles

So,

c² = 323² + 462² + 2(323)(462)cos109 = 104329 + 213444 - 298452cos109

cos109 = -0.3256

So,

c² = 414948.9712

c = 644.1653 miles