Radio transmissions show observers in Houston that the International Space Station is 323 miles away, the Chi- nese space statio
n Tiangong is 462 miles away, and the angle International Space Station–Houston–Tiangong is 109 . How far apart are the two space stations?
1 answer:
Answer:
The two space stations are 644.1653 miles far apart.
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
<u>c = 644.1653 miles</u>
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