SAT Math: Right Triangle Trigonometry Practice Questions
Identify opposite and adjacent sides, use sine, cosine, and tangent, and relate complementary acute angles. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
Answer the questions below — you get instant feedback and a full explanation for each.
1. In a right triangle, an acute angle A has opposite side 9 and adjacent side 12. What is tan A?
Explanation. Tangent is opposite divided by adjacent, so tan A = 9/12 = 3/4. The hypotenuse is not used in the tangent ratio.
2. An acute angle A in a right triangle has sin A = 5/13. What is cos A?
Explanation. Choose opposite side 5 and hypotenuse 13. The adjacent side is sqrt(13^2 - 5^2) = sqrt(144) = 12. Thus cos A = 12/13. The positive root applies because A is acute.
3. The acute angles A and B of a right triangle are complementary. If sin A = 7/25, what is cos B?
Explanation. Since B = 90 degrees - A, cos B = sin A. The sides opposite A and adjacent to B are the same side, so the two ratios both equal 7/25.
4. A 30-60-90 triangle has hypotenuse 18. What is the length of the side opposite the 30-degree angle?
Explanation. The side opposite 30 degrees is half the hypotenuse in a 30-60-90 triangle. Its length is 18/2 = 9.
5. A ladder of length 10 meters makes an angle theta with level ground. If sin theta = 4/5, how high above the ground does the ladder reach, in meters?
Explanation. The ladder is the hypotenuse, and the vertical height is opposite theta. Therefore height/10 = 4/5, so height = 8 meters.
6. In a right triangle with acute angle A, the side adjacent to A has length 8 and cos A = 2/3. What is the hypotenuse length?
Explanation. Cosine equals adjacent divided by hypotenuse: 8/h = 2/3. Cross-multiplying gives 2h = 24, so h = 12. The hypotenuse is longer than the adjacent leg.
📘 Looking for more study material? Browse SAT prep books and study resources. Some links are affiliate links; we may earn a commission at no cost to you.
FAQ
How do I choose a trigonometric ratio?
Relative to the given acute angle, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
Why do complementary angles exchange sine and cosine?
The opposite leg for one acute angle is adjacent to the other. Both angles share the same hypotenuse, so their sine and cosine ratios are exchanged.