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The angles shown above are acute and sin (α°) = cos (b°). If α = 4k − 22 and b = 6k − 13, what is the value of k ?
- a)4.5
- b)5.5
- c)12.5
- d)21.5
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The angles shown above are acute and sin (α°) = cos (b°)...
Choice C is correct. Since the angles are acute and sin(α°) = cos(b°), it follows from the complementary angle property of sines and cosines that α + b = 90. Substituting 4k − 22 for a and 6k − 13 for b gives (4k − 22) + (6k − 13) = 90, which simplifies to 10k − 35 = 90. Therefore, 10k = 125, and k = 12.5.
Choice A is incorrect and may be the result of mistakenly assuming that α + b and making a sign error. Choices B and D are incorrect because they result in values for a and b such that sin(α°) ≠ cos(b°).
Choice A is incorrect and may be the result of mistakenly assuming that α + b and making a sign error. Choices B and D are incorrect because they result in values for a and b such that sin(α°) ≠ cos(b°).
Most Upvoted Answer
The angles shown above are acute and sin (α°) = cos (b°)...
Choice C is correct. Since the angles are acute and sin(α°) = cos(b°), it follows from the complementary angle property of sines and cosines that α + b = 90. Substituting 4k − 22 for a and 6k − 13 for b gives (4k − 22) + (6k − 13) = 90, which simplifies to 10k − 35 = 90. Therefore, 10k = 125, and k = 12.5.
Choice A is incorrect and may be the result of mistakenly assuming that α + b and making a sign error. Choices B and D are incorrect because they result in values for a and b such that sin(α°) ≠ cos(b°).
Choice A is incorrect and may be the result of mistakenly assuming that α + b and making a sign error. Choices B and D are incorrect because they result in values for a and b such that sin(α°) ≠ cos(b°).
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The angles shown above are acute and sin (α°) = cos (b°). If α = 4k − 22 and b = 6k − 13, what is the value of k ?a)4.5b)5.5c)12.5d)21.5Correct answer is option 'C'. Can you explain this answer?
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