Additional Topics in Math

Right Triangle Trigonometry

Use SOH-CAH-TOA and the Pythagorean theorem. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on right triangle trigonometry is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 A right triangle has legs of length 12 and 16. What is the length of the hypotenuse? easy 400-500 Open
2 In a right triangle with legs 5 and 12 and hypotenuse 13, what is the value of sin(A) where A is the… easy 400-500 Open
3 In a right triangle with legs 24 and 45 and hypotenuse 51, what is the value of tan(B) where B is th… easy 400-500 Open
4 A right triangle has legs of length 7 and 24. What is the length of the hypotenuse? easy 400-500 Open
5 In a right triangle with legs 24 and 32 and hypotenuse 40, what is the value of sin(A) where A is th… easy 400-500 Open
6 In a right triangle with legs 18 and 24 and hypotenuse 30, what is the value of tan(B) where B is th… easy 400-500 Open
7 A right triangle has legs of length 9 and 12. What is the length of the hypotenuse? easy 500-600 Open
8 In a right triangle with legs 5 and 12 and hypotenuse 13, what is the value of sin(A) where A is the… easy 500-600 Open
9 In a right triangle with legs 8 and 15 and hypotenuse 17, what is the value of tan(B) where B is the… medium 500-600 Open
10 A right triangle has legs of length 21 and 72. What is the length of the hypotenuse? medium 500-600 Open
11 In a right triangle with legs 12 and 16 and hypotenuse 20, what is the value of sin(A) where A is th… medium 500-600 Open
12 In a right triangle with legs 18 and 24 and hypotenuse 30, what is the value of tan(B) where B is th… medium 500-600 Open
13 A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? medium 600-700 Open
14 In a right triangle with legs 20 and 48 and hypotenuse 52, what is the value of sin(A) where A is th… medium 600-700 Open
15 In a right triangle with legs 8 and 15 and hypotenuse 17, what is the value of tan(B) where B is the… medium 600-700 Open
16 A right triangle has legs of length 7 and 24. What is the length of the hypotenuse? medium 600-700 Open
17 In a right triangle with legs 6 and 8 and hypotenuse 10, what is the value of sin(A) where A is the … medium 600-700 Open
18 In a right triangle with legs 36 and 48 and hypotenuse 60, what is the value of tan(B) where B is th… medium 600-700 Open
19 A right triangle has legs of length 3 and 4. What is the length of the hypotenuse? hard 600-700 Open
20 In a right triangle with legs 20 and 48 and hypotenuse 52, what is the value of sin(A) where A is th… hard 700-800 Open
21 In a right triangle with legs 16 and 30 and hypotenuse 34, what is the value of tan(B) where B is th… hard 700-800 Open
22 A right triangle has legs of length 21 and 72. What is the length of the hypotenuse? hard 700-800 Open
23 In a right triangle with legs 6 and 8 and hypotenuse 10, what is the value of sin(A) where A is the … hard 700-800 Open
24 In a right triangle with legs 9 and 12 and hypotenuse 15, what is the value of tan(B) where B is the… hard 700-800 Open
25 A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? hard 700-800 Open