Before a cargo shuttle descended toward a lunar base, Emek and Tara examined geometric data from the onboard sensors. The system modeled the landing path as a right triangle, showing the shuttle's height, horizontal distance, and approach angle. They used trigonometric ratios to calculate the missing measurements and compare possible landing corridors. Their calculations showed which approach angle avoided the rocky terrain while keeping the descent controlled. By selecting the safest corridor, they guided the shuttle smoothly to the lunar surface.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Identify which two sides are given compared with the angle.
The lunar landing system shows a right triangle where the shuttle height is 600 meters and the horizontal distance to the landing point is 800 meters. Which trigonometric ratio can be used to find the approach angle theta?
tan(theta) = 600/800sin(theta) = 600/800cos(theta) = 600/800tan(theta) = 800/600Correct! Tangent uses the opposite side and adjacent side.
Check the definitions of sine, cosine, and tangent for a right triangle.
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Hint
The direct landing path is the hypotenuse of the right triangle.
A landing corridor is modeled as a right triangle. The shuttle travels 500 meters horizontally and descends 1200 meters vertically. What is the length of the direct landing path in meters?
Correct! The hypotenuse gives the direct distance of the landing path.
Use the Pythagorean theorem to combine the two perpendicular distances.
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Hint
Compare the numerical size of the two angles.
The sensors compare two possible landing corridors. Corridor A has an approach angle of 30 degrees, and Corridor B has an approach angle of 45 degrees. If the terrain requires a steeper descent angle, which corridor should be selected?
Corridor A because 30 degrees is larger than 45 degreesCorridor B because 45 degrees represents the steeper angleCorridor A because smaller angles always mean safer landingsEither corridor because the angles are equalCorrect! A 45 degree angle is steeper than a 30 degree angle.
Compare the angle measures carefully before choosing a corridor.
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