Multiple choice

The angles of elevation of an artificial earth satellite, as measured from two stations which are on the same side are 300 and 600. If the distance between the earth stations is 4000 km. find the height of the satellite : दो भू-स्टेशनों जो एक कृत्रिम उपग्रह के एक ही ओर है से उपग्रह का उन्नयन कोण 300 और 600 मापा जाता है। यदि भू-स्टेशनों के बीच की दूरी 4000 किमी है, तो उपग्रह की ऊँचाई ज्ञात कीजिए।

  1. 6000 km/किमी.

  2. 3296 km/किमी.

  3. 3464 km/किमी.

  4. 4686 km/किमी.

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let satellite height be h. From station 1 (30°): tan30° = h/d₁, from station 2 (60°): tan60° = h/d₂. Distance between stations = d₁ - d₂ = 4000 km. So h/tan30° - h/tan60° = 4000. h(√3 - 1/√3) = 4000. h(3/√3 - 1/√3) = 4000. h(2/√3) = 4000, h = 2000√3 ≈ 3464 km. Option C is correct.