Geometry and TrigonometryVery hardTwo angles whose sine and cosine agree
Geometry and Trigonometry practice question
In a right triangle, the two acute angles measure a° and b°, and sin a° = cos b° = 1/2. What is the value of b − a?
Answer: 30
sin a° = 1/2 for an acute angle means a = 30. The acute angles of a right triangle are complementary, so b = 60 (and indeed cos 60° = 1/2). Then b − a = 60 − 30 = 30.
Common wrong answers
- If you answered 0
- 0 would need a = b, but sin 45° = cos 45° = √2/2, not 1/2.
- If you answered 60
- 60 is b alone; the question asks for the difference b − a.
- If you answered 90
- 90 is a + b, the sum of the two acute angles, not their difference.
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