Geometry and TrigonometryVery hardCosine of the larger acute angle
Geometry and Trigonometry practice question
In a right triangle, the shorter leg is one third as long as the hypotenuse. What is the cosine of the larger acute angle of the triangle?
Answer: 1/3
The larger acute angle is opposite the longer leg, so the leg adjacent to it is the shorter leg: cos = (shorter leg)/(hypotenuse) = 1/3.
Common wrong answers
- If you answered 3
- 3 inverts the ratio; a cosine cannot exceed 1.
- If you answered 2/3
- 2/3 subtracts 1/3 from 1 rather than using the Pythagorean relation.
- If you answered 0.94
- 0.94 is roughly √(8/9), the sine of the larger acute angle.
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