Following a major system update, several communication satellites orbiting the Moon lost their precise alignment, interrupting contact with research stations on the surface. Emek and Tara examined overlapping geometric diagrams showing satellite positions, intersecting communication paths, reference angles, and distance constraints. They combined multiple geometric properties to determine the correct orientation for each satellite while ensuring every communication link remained valid. After checking that the revised configuration satisfied all geometric conditions, they activated the new alignment. Signals immediately stabilized, restoring uninterrupted communication across the entire lunar network.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Same-side interior angles formed by parallel lines are supplementary.
Two parallel reference paths are crossed by a communication beam. One interior angle measures 58°. A second angle lies between the parallel paths on the same side of the beam. What is the measure of the second angle?
58°90°116°122°Correct! The two angles add to 180°, so the second angle is 122°.
Use the supplementary relationship between same-side interior angles.
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Hint
Use Heron's formula after finding the semiperimeter.
Three satellite links form a triangle with side lengths 13 units, 14 units, and 15 units. What is the area of the triangle, in square units?
Correct! The triangular communication region has an area of 84 square units.
Find the semiperimeter first, then apply Heron's formula carefully.
Next🎉 Congrats! You got this question!
Hint
Use the Law of Cosines with sides 10 and 6 and included angle 60°.
Satellite A is 10 units from relay point R, and satellite B is 6 units from R. The angle between links RA and RB is 60°. Which value is the distance between satellites A and B?
2√19 units4√6 units14 units8√3 unitsCorrect! The Law of Cosines gives a distance of 2√19 units.
Square the two known sides, subtract twice their product times cos 60°, and take the square root.
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