The rules that solve most questions
- Pythagorean theorem: a² + b² = c², where c is the hypotenuse, opposite the right angle.
- Common triples and their multiples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.
- SOH-CAH-TOA: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent.
- In a right triangle, sin(A) = cos(B) for the two acute angles A and B.
Traps the wrong answers are built on
- Adding the legs instead of squaring them.
- Using the side opposite the wrong angle.
Worked example
A right triangle has a hypotenuse of length 75 and one leg of length 21. What is the length of the other leg?
- A. 96
- B. 54
- C. 72
- D. 21
Answer: C. Use the Pythagorean theorem: b² = 75² − 21² = 5625 − 441 = 5184. b = √5184 = 72.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Easier
A right triangle has a hypotenuse of length 75 and one leg of length 21. What is the length of the other leg?
Show answer and explanation
Answer: C
Use the Pythagorean theorem: b² = 75² − 21² = 5625 − 441 = 5184.
b = √5184 = 72.
- Question 2Easier
A right triangle has a hypotenuse of length 116 and one leg of length 80. What is the length of the other leg?
Show answer and explanation
Answer: C
Use the Pythagorean theorem: b² = 116² − 80² = 13456 − 6400 = 7056.
b = √7056 = 84.
- Question 3Medium
In right triangle ABC, angle C is the right angle, BC = 20, AC = 21 and AB = 29. What is the value of sin(A)?
Show answer and explanation
Answer: A
For angle A, the opposite side is BC = 20, the adjacent side is AC = 21 and the hypotenuse is AB = 29.
sin(A) = opposite/hypotenuse = 20/29.
- Question 4Medium
In right triangle ABC, angle C is the right angle, BC = 9, AC = 12 and AB = 15. What is the value of tan(A)?
Show answer and explanation
Answer: A
For angle A, the opposite side is BC = 9, the adjacent side is AC = 12 and the hypotenuse is AB = 15.
tan(A) = opposite/adjacent = 9/12 = 3/4.
- Question 5Easier
A right triangle has a hypotenuse of length 52 and one leg of length 20. What is the length of the other leg?
Show answer and explanation
Answer: D
Use the Pythagorean theorem: b² = 52² − 20² = 2704 − 400 = 2304.
b = √2304 = 48.
- Question 6Medium
In right triangle ABC, angle C is the right angle, BC = 10, AC = 24 and AB = 26. What is the value of tan(A)?
Show answer and explanation
Answer: C
For angle A, the opposite side is BC = 10, the adjacent side is AC = 24 and the hypotenuse is AB = 26.
tan(A) = opposite/adjacent = 10/24 = 5/12.
- Question 7Medium
In right triangle ABC, angle C is the right angle, BC = 14, AC = 48 and AB = 50. What is the value of tan(A)?
Show answer and explanation
Answer: B
For angle A, the opposite side is BC = 14, the adjacent side is AC = 48 and the hypotenuse is AB = 50.
tan(A) = opposite/adjacent = 14/48 = 7/24.
- Question 8Easier
A right triangle has a hypotenuse of length 50 and one leg of length 14. What is the length of the other leg?
Show answer and explanation
Answer: A
Use the Pythagorean theorem: b² = 50² − 14² = 2500 − 196 = 2304.
b = √2304 = 48.
- Question 9Medium
In right triangle ABC, angle C is the right angle, BC = 28, AC = 96 and AB = 100. What is the value of tan(A)?
Show answer and explanation
Answer: D
For angle A, the opposite side is BC = 28, the adjacent side is AC = 96 and the hypotenuse is AB = 100.
tan(A) = opposite/adjacent = 28/96 = 7/24.
- Question 10Medium
In right triangle ABC, angle C is the right angle, BC = 24, AC = 45 and AB = 51. What is the value of cos(A)?
Show answer and explanation
Answer: B
For angle A, the opposite side is BC = 24, the adjacent side is AC = 45 and the hypotenuse is AB = 51.
cos(A) = adjacent/hypotenuse = 45/51 = 15/17.
More Geometry and Trigonometry practice
Questions people ask
Is this right triangles and trigonometry practice like the real SAT?
The questions follow the format of the digital SAT's Geometry and Trigonometry domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Geometry and Trigonometry is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Problem-Solving and Data Analysis.