Trigonometry: Practice Questions with AnswersCurriculum: TrigonometryGrades: 10–12Questions: 12Mode: Practice These are the real questions from this STEPCAI practice lesson. Read each question, pick your answer, then open Show the answer to check yourself and read why it is right. On STEPCAI the same lesson runs interactively: you click an answer and get instant feedback, and a free account keeps your scores. 1. In a right triangle, the sine of an acute angle equals the length of which side divided by the length of the hypotenuse?- The adjacent side
- The other leg squared
- The opposite side
- The hypotenuse itself
Show the answerAnswer: C. The opposite side
Sine is defined as opposite over hypotenuse, often remembered with SOH in the memory aid SOH-CAH-TOA. 2. Which ratio correctly defines the cosine of an acute angle in a right triangle?- opposite/adjacent
- adjacent/hypotenuse
- opposite/hypotenuse
- hypotenuse/adjacent
Show the answerAnswer: B. adjacent/hypotenuse
Cosine is defined as adjacent over hypotenuse, the CAH part of SOH-CAH-TOA. 3. Which ratio correctly defines the tangent of an acute angle in a right triangle?- hypotenuse/opposite
- opposite/hypotenuse
- opposite/adjacent
- adjacent/opposite
Show the answerAnswer: C. opposite/adjacent
Tangent is defined as opposite over adjacent, the TOA part of SOH-CAH-TOA, and it can also be found as sine divided by cosine. 4. How many degrees are in a right angle?- 45 degrees
- 180 degrees
- 90 degrees
- 60 degrees
Show the answerAnswer: C. 90 degrees
A right angle measures exactly 90 degrees and is marked with a small square symbol in diagrams. 5. What is the sum of the interior angles of any triangle?- 180 degrees
- 270 degrees
- 360 degrees
- 90 degrees
Show the answerAnswer: A. 180 degrees
The three interior angles of any triangle always add up to 180 degrees, regardless of the triangle's shape. 6. What is 180 degrees converted to radians?- 2 pi radians
- pi/2 radians
- pi/4 radians
- pi radians
Show the answerAnswer: D. pi radians
The conversion factor is pi radians equals 180 degrees, so 180 degrees converts directly to pi radians. 7. What is pi/2 radians converted to degrees?- 60 degrees
- 90 degrees
- 45 degrees
- 180 degrees
Show the answerAnswer: B. 90 degrees
Since pi radians equals 180 degrees, pi/2 radians is half of that, which equals 90 degrees. 8. What is the exact value of sin(30 degrees)?- 1/2
- 1
- square root of 2 over 2
- square root of 3 over 2
Show the answerAnswer: A. 1/2
sin(30 degrees) equals 1/2, one of the standard values that comes from the 30-60-90 special right triangle. 9. What is the exact value of cos(60 degrees)?- square root of 2 over 2
- square root of 3 over 2
- 1/2
- 1
Show the answerAnswer: C. 1/2
cos(60 degrees) equals 1/2, found from the 30-60-90 special right triangle where the side adjacent to the 60 degree angle is the shortest leg. 10. What is the exact value of tan(45 degrees)?- undefined
- square root of 2
- 1
- 0
Show the answerAnswer: C. 1
In a 45-45-90 triangle the two legs are equal in length, so opposite divided by adjacent equals 1. 11. According to the Pythagorean theorem, if a and b are the legs of a right triangle and c is the hypotenuse, which equation is true?- a * b = c^2
- a^2 - b^2 = c^2
- a^2 + b^2 = c^2
- a + b = c
Show the answerAnswer: C. a^2 + b^2 = c^2
The Pythagorean theorem states a^2 + b^2 = c^2, relating the squares of the two legs to the square of the hypotenuse in any right triangle. 12. In a right triangle, which side is the hypotenuse?- The side opposite the right angle
- The side adjacent to the smallest angle
- Either of the two legs
- The shortest side
Show the answerAnswer: A. The side opposite the right angle
The hypotenuse is always the longest side of a right triangle and is located directly across from the 90 degree angle. More free high school sample lessonsSee all free sample lessons »
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