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Trigonometry — ISEE Upper practice questions

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Practice 129 Trigonometry questions in the app

What this topic is

Trigonometry questions at this level work with right triangles and the three basic ratios: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

A typical item gives one acute angle and one side, then asks which expression equals another side. Choices look alike, such as a length multiplied by the sine of the angle or divided by its cosine, so the work is identifying which sides are opposite and adjacent to the given angle.

No calculator is needed because the expression, not a decimal, is the answer. Remembering SOH-CAH-TOA keeps the ratios straight.

Sample questions

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

Question 1Harder

A right triangle $N O P$ has a right angle at $O$ . Side $\overline{O P}$ measures 16 centimeters, and $∠ P N O$ measures $4 2^{\circ}$ . Which expression is equal to the length of $\overline{N P}$ ?

\frac{16}{\sin 4 2^{\circ}}

✓ Correct

\frac{\sin 4 2^{\circ}}{16}

✗ Not this one

16 \sin 4 2^{\circ}

✗ Not this one

\frac{16}{\cos 4 2^{\circ}}

✗ Not this one

Show answer

Answer: A — $\frac{16}{\sin 4 2^{\circ}}$

Side $O P$ is opposite the $4 2^{\circ}$ angle and $N P$ is the hypotenuse, so $\sin 4 2^{\circ} = \frac{16}{N P}$ . Solving for $N P$ gives $\frac{16}{\sin 4 2^{\circ}}$ .

Question 2Mid

Right triangle $G H J$ has a right angle at $H$ . The length of $\overline{G J}$ is 14 meters, and the measure of $∠ J G H$ is $1 9^{\circ}$ . Which expression is equal to the length, in meters, of $\overline{G H}$ ?

14 \sin 1 9^{\circ}

✗ Not this one

14 \cos 1 9^{\circ}

✓ Correct

\frac{14}{\cos 1 9^{\circ}}

✗ Not this one

\frac{\cos 1 9^{\circ}}{14}

✗ Not this one

Show answer

Answer: B — $14 \cos 1 9^{\circ}$

Side $G H$ is adjacent to the $1 9^{\circ}$ angle and $G J$ is the hypotenuse, so $\cos 1 9^{\circ} = \frac{G H}{14}$ . Therefore $G H = 14 \cos 1 9^{\circ}$ .

Question 3Mid

In right triangle $R S T$ , $∠ R S T$ is a right angle, $∠ S R T$ measures $2 7^{\circ}$ , and the length of $\overline{R T}$ is 13 feet. Which of the expressions in the answer choices is equal to the length of $\overline{S T}$ ?

\frac{\sin 2 7^{\circ}}{13}

✗ Not this one

\frac{13}{\sin 2 7^{\circ}}

✗ Not this one

13 \cos 2 7^{\circ}

✗ Not this one

13 \sin 2 7^{\circ}

✓ Correct

Show answer

Answer: D — $13 \sin 2 7^{\circ}$

Side $S T$ is opposite the $2 7^{\circ}$ angle and $R T$ is the hypotenuse, so $\sin 2 7^{\circ} = \frac{S T}{13}$ . Therefore $S T = 13 \sin 2 7^{\circ}$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 129 Trigonometry questions in the app

Trigonometry — ISEE Upper practice questions

What this topic is

Sample questions

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