Right triangles and trigonometry — SAT practice questions

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Practice 71 Right triangles and trigonometry questions in the app

What this topic is

Right triangles and trigonometry questions combine the Pythagorean theorem, special right triangles, and the ratios sine, cosine and tangent.

Sides that satisfy a^2 + b^2 = c^2 form a right triangle, which also identifies its largest angle as the right angle. In an isosceles right triangle the hypotenuse is a leg times the square root of two, and a triangle with angles of thirty, sixty and ninety degrees has sides in the ratio one to root three to two.

Sine is opposite over hypotenuse, and the sine of one acute angle equals the cosine of the other, a fact questions test directly. Answers are often exact values containing radicals.

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?

It is acute.✗ Not this oneIt is a right angle.✓ CorrectIt is obtuse.✗ Not this oneIt cannot be determined.✗ Not this one

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Answer: B — It is a right angle.

Since $8^{2} + 1 5^{2} = 1 7^{2}$ , 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?

31 + 31 \sqrt{2}

✗ Not this one

62 \sqrt{2}

✗ Not this one124✗ Not this one

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 $A B C$ , angle $B$ is a right angle and $\sin A = \frac{1}{2}$ . What is the value of $\cos A$ ?

\frac{1}{2}

✗ Not this one

\frac{\sqrt{2}}{2}

✗ Not this one

\frac{\sqrt{3}}{2}

✓ Correct

\frac{\sqrt{3}}{3}

✗ Not this one

Show answer

Answer: C — $\frac{\sqrt{3}}{2}$

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

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Practice 71 Right triangles and trigonometry questions in the app

Right triangles and trigonometry — SAT practice questions

What this topic is

Sample questions

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