Example 1 Easy
In a right triangle, the side opposite angle theta is 6 and the hypotenuse is 10. What is sin(theta)?
- 3/5
- 4/5
- 5/3
- 5/4
Show answer and explanation
Answer: 3/5
Sine is opposite over hypotenuse, so sin(theta) = 6/10 = 3/5.
SAT Math skill page
SAT Trigonometry Practice
Use side ratios and special-triangle patterns to connect angles with missing lengths.
12-18 min practice time 3 examples on page Geometry and Trigonometry
What this tests
What to know for this SAT skill
- Choose sine, cosine, or tangent from the given sides
- Use trigonometric ratios to find a missing length
- Recognize 30-60-90 and 45-45-90 triangle ratios
- Keep opposite and adjacent sides tied to the marked angle
Practice examples
Try a few SAT-style questions
Example 2 Medium
For angle theta, tan(theta) = 3/4. If the adjacent leg is 12, what is the opposite leg?
- 4
- 9
- 16
- 36
Show answer and explanation
Answer: 9
Tangent is opposite over adjacent. Set x/12 = 3/4 and solve to get x = 9.
Example 3 Hard
A 30-60-90 triangle has a shortest side of length 5. What is the hypotenuse?
- 5 square root 2
- 5 square root 3
- 10
- 15
Show answer and explanation
Answer: 10
The side ratio is 1 : square root 3 : 2, so the hypotenuse is twice the shortest side.
Quick drills
Practice this skill from more angles
Choose sine, cosine, or tangent from the given sides
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Use trigonometric ratios to find a missing length
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Recognize 30-60-90 and 45-45-90 triangle ratios
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Keep opposite and adjacent sides tied to the marked angle
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
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.
Study plan
How to practice this skill in Dolphin
- Mark the right angle, hypotenuse, and reference angle.
- Label the opposite and adjacent legs relative to that angle.
- Choose the ratio that uses the known side and requested side.
- Estimate the result to confirm the side length is reasonable.
Related practice
Build the surrounding skills
Skill cluster
Keep practicing SAT Math
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 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.