After a meteor shower disrupted an orbital communication tower around a distant planet, Emek and Tara entered the guidance system to repair the antenna alignment. The system displayed right triangles representing the antenna position, including measured sides and unknown angles. They used trigonometric ratios such as sine, cosine, and tangent to calculate the missing values and determine the correct orientation. After adjusting the antenna to the calculated angle, they restored the signal path and reestablished communication with the exploration fleet.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Think about which two sides are given compared with the angle.
The antenna guidance system shows a right triangle where the side opposite an angle is 12 meters and the hypotenuse is 20 meters. Which trigonometric ratio should Emek and Tara use to find the angle?
sinecosinetangentsecantCorrect! Sine relates the opposite side and the hypotenuse.
Check which trigonometric ratio uses the two sides given in the problem.
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Hint
Use the Pythagorean theorem to find the missing side of a right triangle.
The antenna forms a right triangle with a horizontal distance of 15 meters and a vertical height of 20 meters. What is the length of the antenna support beam in meters?
Correct! The support beam length is the hypotenuse of the right triangle.
Use the relationship between the two legs and the hypotenuse of a right triangle.
Next🎉 Congrats! You got this question!
Hint
Identify the ratio that uses the adjacent side and hypotenuse.
The guidance system shows a right triangle for the antenna orientation. The adjacent side to the angle is 18 meters and the hypotenuse is 30 meters. Which equation can be used to find the angle theta?
sin(theta) = 18/30cos(theta) = 18/30tan(theta) = 18/30cos(theta) = 30/18Correct! Cosine is the ratio of adjacent side to hypotenuse.
Review the definitions of sine, cosine, and tangent for right triangles.
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