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Right triangles and trigonometry — SAT practice questions

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Practice 68 Right triangles and trigonometry questions in the app

What this topic is

Right triangles and trigonometry on the SAT Math test covers the Pythagorean theorem, special right triangles, and sine, cosine, and tangent.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A triangle has side lengths 8, 15, and 17. Which of the following describes the largest angle of the triangle?

AIt is acute.✗ Not this oneBIt is a right angle.✓ CorrectCIt is obtuse.✗ Not this oneDIt cannot be determined.✗ Not this one

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Answer: B — It is a right angle.

Since $8^2+15^2=17^2$, the angle opposite the side of length 17 is a right angle.

Question 2Mid

A square with side length $31\sqrt{2}$ units is cut along a diagonal, producing two isosceles right triangles. What is the perimeter, in units, of either triangle?

A$31+31\sqrt{2}$✗ Not this oneB$62\sqrt{2}$✗ Not this oneC124✗ Not this oneD$62+62\sqrt{2}$✓ Correct

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Answer: D — $62+62\sqrt{2}$

Each triangle has two legs of length $31\sqrt{2}$, and its hypotenuse, the square’s diagonal, has length $(31\sqrt{2})(\sqrt{2})=62$. The perimeter is $62\sqrt{2}+62$.

Question 3Mid

In right triangle $ABC$, angle $B$ is a right angle and $\sin A=\dfrac{1}{2}$. What is the value of $\cos A$?

A$\dfrac{1}{2}$✗ Not this oneB$\dfrac{\sqrt{2}}{2}$✗ Not this oneC$\dfrac{\sqrt{3}}{2}$✓ CorrectD$\dfrac{\sqrt{3}}{3}$✗ Not this one

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Answer: C — $\dfrac{\sqrt{3}}{2}$

With opposite 1 and hypotenuse 2, the adjacent leg is $\sqrt{3}$, so $\cos A=\dfrac{\sqrt3}{2}$.

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