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SAT Math skill page

SAT Trigonometry Practice

Use side ratios and special-triangle patterns to connect angles with missing lengths.

Practice trigonometry in Dolphin SATPractice questions
12-18 min practice time3 questions on pageGeometry and Trigonometry
Practice time12-18 min
Question bank3 questions
Best forGeometry and Trigonometry

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
In a right triangle, the side opposite angle theta is 6 and the hypotenuse is 10. What is sin(theta)?
  1. 3/5
  2. 4/5
  3. 5/3
  4. 5/4
Show answer and solution
Correct answerA. 3/5

Solution walkthrough

  1. Sine is opposite over hypotenuse, so sin(theta) = 6/10 = 3/5.
Question 2 of 3Medium
For angle theta, tan(theta) = 3/4. If the adjacent leg is 12, what is the opposite leg?
  1. 4
  2. 9
  3. 16
  4. 36
Show answer and solution
Correct answerB. 9

Solution walkthrough

  1. Tangent is opposite over adjacent.
  2. Set x/12 = 3/4 and solve to get x = 9.
Question 3 of 3Hard
A 30-60-90 triangle has a shortest side of length 5. What is the hypotenuse?
  1. 5 square root 2
  2. 5 square root 3
  3. 10
  4. 15
Show answer and solution
Correct answerC. 10

Solution walkthrough

  1. The side ratio is 1 : square root 3 : 2, so the hypotenuse is twice the shortest side.

Avoid these traps

Common mistakes on this skill

Using the wrong side ratio

Label opposite, adjacent, and hypotenuse relative to the marked angle before choosing a trig function.

Changing the reference angle

Opposite and adjacent switch when the reference angle changes, even though the triangle stays the same.

Mixing up special-triangle ratios

Write the 30-60-90 or 45-45-90 ratio before scaling it to the given side.

Treating degrees and radians as interchangeable

Use 180 degrees = pi radians, then multiply by pi/180 to convert a degree measure to radians.

Study plan

How to practice this skill in Dolphin

  1. Mark the right angle, hypotenuse, and reference angle.
  2. Label the opposite and adjacent legs relative to that angle.
  3. Choose the ratio that uses the known side and requested side.
  4. If the angle uses degrees or radians, convert with 180 degrees = pi radians before solving.
  5. Estimate the result to confirm the side length is reasonable.
Practice trigonometry in Dolphin SAT

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FAQ

Questions about SAT Trigonometry Practice

Which trigonometry functions are tested on the SAT?

SAT questions can use sine, cosine, and tangent, along with special right-triangle relationships.

Do I need to memorize SOH-CAH-TOA?

It is a useful shortcut for remembering the three side ratios, even though the SAT provides some geometry formulas.

How do I convert degrees to radians?

Multiply the degree measure by pi/180. To convert radians to degrees, multiply by 180/pi.

How is this different from the right-triangles page?

The right-triangles page focuses on side lengths and the Pythagorean theorem. This page focuses specifically on angle-based trig ratios.