The path of a satellite orbiting the earth causes it to pass directly over two t

Question

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 49 km apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.8° and 84.4, respectively 844 88 NOTE: The picture is NOT drawn to scale. How far is the satellite from station A? distance from A- How high is the satellite above the ground? height km km Enter your answer as a number; your answer should be accurate to 2 decimal places Get help: Video Points possible: 1 This is attempt 1 of 2. Submit

Explanation / Answer

dropping a perpendicular from satellite to the ground

tan 87.8 = h / d

h = d tan 87.8

h = 26.03 d

applying tan rule on 2nd triangle

tan 84.4 = h / ( d + 49 )

h = ( d + 49 ) tan 84.4

h = 10.20d + 499.74

10.20d + 499.74 = 26.03 d  

d = 31.57

cos 87.8 = 31.57 / x

x = 822.40

so, satellite A is 822.40 km from A

height = 821.77 km

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