20 easy SAT Right triangles & trigonometry questions
These are the questions most test-takers get right. They are worth practising anyway: on the digital SAT the easy questions in Module 1 are what route you into the harder, higher-scoring Module 2, so dropping one costs more than it looks.
Every question below is a real item from the SAT Climb bank, tagged easy by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Geometry and Trigonometry~1 per testEasy tier
A right triangle has legs of length a and b and hypotenuse of length c. If a=8 and c=17, what is the value of b?
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Why C is right
By the Pythagorean theorem, a2 + b2 = c2. Substituting the given values: 82 + b2 = 172, so 64 + b2 = 289, which gives b2 = 225 and b=15.
Why the others are wrong
AThis incorrectly subtracts 8 from 17 instead of using the Pythagorean theorem.
BThis incorrectly adds the squares instead of subtracting: 17² - 8² was computed as 17² + 8².
DThis uses the other common Pythagorean triple (5-12-13) instead of solving for this triangle.
Question 2Easy
In a right triangle, the measure of one acute angle is y°. The length of the hypotenuse is 17 and the length of the leg opposite the angle with measure y° is 15. What is the value of sin y°?
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Why C is right
The sine of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Since the opposite side is 15 and the hypotenuse is 17, sin y° = 15/17.
Why the others are wrong
AThis results from using the adjacent leg (8, found by the Pythagorean theorem) instead of the opposite leg in the ratio, confusing sine with cosine.
BThis results from incorrectly using the adjacent leg in the numerator and the opposite leg in the denominator, swapping the roles of opposite and adjacent.
DThis results from inverting the sine ratio, placing the hypotenuse in the numerator instead of the denominator.
Question 3Easy
In a right triangle, one angle measures 60°. The length of the side adjacent to the 60° angle is 4. What is the length of the side opposite the 60° angle?
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Why C is right
In a 30-60-90 triangle, the side opposite 60° is 3 times the side opposite 30°. The side adjacent to 60° is the side opposite 30°, so the side opposite 60° is 43.
Why the others are wrong
AThis incorrectly divides the adjacent side by 2 instead of multiplying by √3.
BThis incorrectly doubles the adjacent side instead of applying the √3 ratio.
DThis incorrectly assumes the two legs are equal, missing the special 30-60-90 ratio.
Question 4Easy
In a right triangle, the hypotenuse has length 13 and one leg has length 5. What is the length of the other leg?
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Why C is right
By the Pythagorean theorem, if the hypotenuse has length 13 and one leg has length 5, then 52 + b2 = 132. Solving, 25 + b2 = 169, so b2 = 144 and b=12.
Why the others are wrong
AThis results from subtracting the given leg from the hypotenuse (13 - 5 = 8) instead of using the Pythagorean theorem.
BThis results from adding the hypotenuse and leg (13 + 5 = 18) instead of using the Pythagorean theorem.
DThis results from multiplying the hypotenuse and leg (13 × 5 = 65) instead of using the Pythagorean theorem.
Question 5Easy
A right triangle has a hypotenuse of length 25 and one leg of length 7. What is the length of the other leg?
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Why D is right
By the Pythagorean theorem, the sum of the squares of the legs equals the square of the hypotenuse. Therefore, 72 + b2 = 252, which gives 49 + b2 = 625, so b2 = 576 and b=24.
Why the others are wrong
AThis incorrectly subtracts 7 from 25 instead of using the Pythagorean theorem.
BThis incorrectly adds the squares instead of subtracting: 25² + 7² instead of 25² - 7².
CThis results from using a different Pythagorean triple (3-4-5 scaled) instead of solving this problem.
Question 6Easy
Triangle DEF has a right angle at E. The measure of angle D is w°. If DE = 12 and DF = 13, what is the value of cos w°?
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Why A is right
The cosine of an acute angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. Since the right angle is at E, DF is the hypotenuse and DE is adjacent to angle D. Therefore, cos w° = 12/13.
Why the others are wrong
BThis results from using the opposite side instead of the adjacent side in the cosine ratio.
CThis results from inverting the cosine ratio, using hypotenuse over adjacent.
DThis results from using the tangent ratio instead of cosine.
Question 7Easy
In a right triangle, the measure of one acute angle is 60°. The length of the leg adjacent to this angle is 8. What is the length of the leg opposite this angle?
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Why C is right
In a 30-60-90 triangle, the sides are in the ratio 1 : 3 : 2. The leg adjacent to the 60° angle corresponds to the shorter leg (length 1 in the ratio), so if the adjacent leg is 8, the opposite leg is 83.
Why the others are wrong
AThis results from incorrectly dividing the adjacent leg by 2, not recognizing the special ratio for a 30-60-90 triangle.
BThis results from incorrectly treating the opposite and adjacent legs as equal, confusing the 60° angle with a 45° angle.
DThis is the hypotenuse length for this 30-60-90 triangle, not the opposite leg.
Question 8Easy
A right triangle has a hypotenuse of length 17 and one leg of length 15. What is the length of the other leg?
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Why D is right
By the Pythagorean theorem, if the hypotenuse has length 17 and one leg has length 15, then 152 + b2 = 172. Solving, 225 + b2 = 289, so b2 = 64 and b=8.
Why the others are wrong
AThis results from subtracting the leg from the hypotenuse (17 - 15 = 2) instead of using the Pythagorean theorem.
BThis results from adding the hypotenuse and leg (17 + 15 = 32) instead of using the Pythagorean theorem.
CThis results from multiplying the hypotenuse and leg (17 × 15 = 255) instead of using the Pythagorean theorem.
Question 9Easy
Triangle ABC is a right triangle with the right angle at C. The length of side AB is 17, and the length of side BC is 15. What is the length of side AC?
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Why B is right
Since the right angle is at C, side AB is the hypotenuse. By the Pythagorean theorem, AC2 + BC2 = AB2, so AC2 + 152=172. Therefore, AC2 = 289 - 225 = 64, so AC = 8.
Why the others are wrong
AThis results from subtracting the leg from the hypotenuse without applying the Pythagorean theorem.
CThis results from adding the squares instead of finding the difference.
DThis results from incorrectly calculating 17² + 15² instead of 17² - 15².
Question 10Easy
In a right triangle, the length of one leg is 3 and the length of the other leg is 4. What is the length of the hypotenuse?
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Why B is right
By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the two legs. Therefore, c2 = 32+42=9+16=25, so c=5.
Why the others are wrong
AThis is the sum of the two legs, not the hypotenuse. The Pythagorean theorem requires squaring the legs, summing, then taking the square root.
CThis results from incorrectly multiplying the two legs together instead of using the Pythagorean theorem.
DThis is the value of c² before taking the square root to find the hypotenuse length.
Question 11Easy
In a right triangle, the length of one leg is 5 and the length of the other leg is 12. What is the length of the hypotenuse?
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Why C is right
By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs. Therefore, c2 = 52+122=25+144=169, so c=13.
Why the others are wrong
AThis results from subtracting the legs instead of applying the Pythagorean theorem.
BThis results from adding the legs directly without squaring them.
DThis results from incorrectly applying the relationship between the sides.
Question 12Easy
In a right triangle, one acute angle measures 60° and the side opposite this angle has length 6. What is the length of the side adjacent to the 60° angle?
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Why D is right
In a 30-60-90 triangle, if the side opposite the 60° angle has length 6, then this side equals the short leg times 3. So the short leg (adjacent to the 60° angle) is 6/3=23.
Why the others are wrong
AThis incorrectly uses the 30-60-90 ratio by halving the opposite side.
BThis multiplies the opposite side by √3 instead of dividing, confusing which side is longer.
CThis incorrectly doubles the opposite side to find the hypotenuse and misidentifies it as the adjacent side.
Question 13Easy
In a right triangle, the lengths of the two legs are 5 and 12. What is the length of the hypotenuse?
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Why C is right
By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs. Therefore, c2 = 52+122=25+144=169, so c=13.
Why the others are wrong
AThis incorrectly subtracts the leg lengths instead of using the Pythagorean theorem.
BThis incorrectly adds the leg lengths instead of summing their squares.
DThis results from an arithmetic error in computing the square root.
Question 14Easy
In a right triangle, one leg has length 8 and the other leg has length 15. What is the length of the hypotenuse?
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Why A is right
By the Pythagorean theorem, the sum of the squares of the two legs equals the square of the hypotenuse. Thus 82+152 = c2, which gives 64 + 225 = 289, so c=17.
Why the others are wrong
BThis choice results from adding the leg lengths instead of using the Pythagorean theorem.
CThis choice results from subtracting the leg lengths instead of applying the correct formula.
DThis choice results from multiplying the leg lengths instead of using the Pythagorean theorem.
Question 15Easy
In a right triangle, one leg has length 6 and the other leg has length 8. What is the length of the hypotenuse?
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Why B is right
By the Pythagorean theorem, the sum of the squares of the two legs equals the square of the hypotenuse. Thus 62+82 = c2, which gives 36 + 64 = 100, so c=10.
Why the others are wrong
AThis choice results from adding the leg lengths instead of using the Pythagorean theorem.
CThis choice results from multiplying the leg lengths instead of applying the correct formula.
DThis choice results from subtracting the leg lengths instead of using the Pythagorean theorem.
Question 16Easy
A right triangle has one leg of length 7 and a hypotenuse of length 25. What is the length of the other leg?
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Why B is right
By the Pythagorean theorem, 72 + b2 = 252, which gives 49 + b2 = 625. Solving for b gives b2 = 576, so b=24.
Why the others are wrong
AThis choice results from adding the given leg and hypotenuse instead of applying the Pythagorean theorem.
CThis choice results from incorrectly subtracting the given leg from the hypotenuse.
DThis choice results from multiplying the given values instead of using the correct formula.
Question 17Easy
In a right triangle, the hypotenuse has length 5 and one leg has length 3. What is the length of the other leg?
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Why C is right
By the Pythagorean theorem, 32 + b2 = 52, so 9 + b2 = 25. Therefore, b2 = 16 and b=4.
Why the others are wrong
AThis represents the difference between the hypotenuse and the given leg rather than applying the Pythagorean theorem.
BThis incorrectly adds the squares: 5² + 3² = 34, then approximates to 8.
DThis incorrectly assumes the other leg equals the hypotenuse rather than computing from the given values.
Question 18Easy
In a right triangle, the length of one leg is 5 and the length of the hypotenuse is 13. What is the value of the length of the other leg?
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Why A is right
Using the Pythagorean theorem, if a and b are the legs and c is the hypotenuse, then a2 + b2 = c2. Substituting: 52 + b2 = 132, so 25 + b2 = 169. Solving gives b2 = 144, and therefore b=12.
Why the others are wrong
BThis results from subtracting the given leg from the hypotenuse instead of using the Pythagorean theorem.
CThis results from adding the given leg and hypotenuse instead of using the correct formula.
DThis is the value of b² before taking the square root to find the leg length.
Question 19Easy
In a right triangle, the measure of one acute angle is x°. The length of the side opposite the angle with measure x° is 5, and the length of the side adjacent to the angle with measure x° is 12. What is the value of sin x°?
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Why A is right
The sine of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. The hypotenuse has length √([MATH]52+122)[/MATH] = 25+144=13. Therefore, sinx∘=5/13.
Why the others are wrong
BThis is the cosine of x°, not the sine. The cosine uses the adjacent side rather than the opposite side.
CThis is the tangent of the angle formed by swapping opposite and adjacent sides.
DThis is the tangent of x°, which uses opposite over adjacent, but fails to recognize that sine requires the hypotenuse in the denominator.
Question 20Easy
In a right triangle, the measure of one acute angle is z°. The length of the leg opposite the angle with measure z° is 12, and the length of the hypotenuse is 13. What is the value of cos z°?
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Why A is right
The cosine of an acute angle in a right triangle is the ratio of the adjacent leg to the hypotenuse. Using the Pythagorean theorem, the adjacent leg is √([MATH]132−122)[/MATH] = 169−144=25=5. Therefore, cosz∘=5/13.
Why the others are wrong
BThis results from using sin z° (opposite/hypotenuse) instead of cos z° (adjacent/hypotenuse).
CThis results from incorrectly using the opposite leg as the denominator instead of the hypotenuse.
DThis results from inverting the ratio and using the opposite leg instead of the adjacent leg.
What to do after easy
Getting these right quickly is the point: speed on the easy questions is what buys time for the hard ones. When they stop costing you effort, move up.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.