Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 so they can later determine its size. The distance between the satellites is 900 km. If KA-1212's camera is focused on SAL-11, it must rotate 60° to see the UFO. If SAL-11's camera is focused on KA-1212, it must rotate 75° to see the UFO. How far is the UFO from KA-1212? Round your answer to the nearest kilometer.

Question

Jakob Holland

Mathematics

13 December, 22:20

Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 so they can later determine its size. The distance between the satellites is 900 km. If KA-1212's camera is focused on SAL-11, it must rotate 60° to see the UFO. If SAL-11's camera is focused on KA-1212, it must rotate 75° to see the UFO. How far is the UFO from KA-1212? Round your answer to the nearest kilometer.

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Answers (1)

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Joey Bolton · Answer 1

Use the sine rule. The two satellites form the base of a triangle with the UFO at the vertex. The sides of the triangle are KA-1212 joined to the UFO, and we call this side k, and the third side is SAL-11 joined to the UFO. The vertex angle is 180 - (60+75) = 45.

k/sin75=900/sin45 so k=900sin75/sin45=1229km approx.