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Mathematics Achievement

Trigonometry — ISEE Upper practice questions

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129 practice questions in the app
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Practice 129 Trigonometry questions in the app

What this topic is

Trigonometry on the ISEE Upper Mathematics Achievement section covers right-triangle sine, cosine, and tangent.

A student must identify the opposite side, adjacent side, and hypotenuse relative to a named acute angle and select the expression that equals a missing length. Questions typically present a right triangle with a right angle at a labeled vertex, give one side length and one angle measure, and ask which expression equals another side.

Answer choices are trigonometric expressions rather than decimal lengths. Common traps include swapping sine with cosine, using the complementary angle, or treating a given leg as the hypotenuse.

Sample questions

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

Question 1Harder

A right triangle $NOP$ has a right angle at $O$ . Side $\overline{OP}$ measures 16 centimeters, and $\angle PNO$ measures $42^\circ$ . Which expression is equal to the length of $\overline{NP}$ ?

\dfrac{16}{\sin 42^\circ}

✓ Correct

\dfrac{\sin 42^\circ}{16}

✗ Not this one

16\sin 42^\circ

✗ Not this one

\dfrac{16}{\cos 42^\circ}

✗ Not this one

Show answer

Answer: A — $\dfrac{16}{\sin 42^\circ}$

Side $OP$ is opposite the $42^\circ$ angle and $NP$ is the hypotenuse, so $\sin 42^\circ=\dfrac{16}{NP}$ . Solving for $NP$ gives $\dfrac{16}{\sin 42^\circ}$ .

Question 2Mid

Right triangle $GHJ$ has a right angle at $H$ . The length of $\overline{GJ}$ is 14 meters, and the measure of $\angle JGH$ is $19^\circ$ . Which expression is equal to the length, in meters, of $\overline{GH}$ ?

14\sin 19^\circ

✗ Not this one

14\cos 19^\circ

✓ Correct

\dfrac{14}{\cos 19^\circ}

✗ Not this one

\dfrac{\cos 19^\circ}{14}

✗ Not this one

Show answer

Answer: B — $14\cos 19^\circ$

Side $GH$ is adjacent to the $19^\circ$ angle and $GJ$ is the hypotenuse, so $\cos 19^\circ=\dfrac{GH}{14}$ . Therefore $GH=14\cos 19^\circ$ .

Question 3Mid

In right triangle $RST$ , $\angle RST$ is a right angle, $\angle SRT$ measures $27^\circ$ , and the length of $\overline{RT}$ is 13 feet. Which of the expressions in the answer choices is equal to the length of $\overline{ST}$ ?

\dfrac{\sin 27^\circ}{13}

✗ Not this one

\dfrac{13}{\sin 27^\circ}

✗ Not this one

13\cos 27^\circ

✗ Not this one

13\sin 27^\circ

✓ Correct

Show answer

Answer: D — $13\sin 27^\circ$

Side $ST$ is opposite the $27^\circ$ angle and $RT$ is the hypotenuse, so $\sin 27^\circ=\dfrac{ST}{13}$ . Therefore $ST=13\sin 27^\circ$ .

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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