11th Grade Trigonometry Practice: Questions, Answers and Tips

Looking for 11th grade trigonometry practice? Below are worked examples, the mistakes students make most, and practice questions with an answer key.

Every example below comes from BAMS Academy's Trigonometry practice, the same questions students answer on the site.

Trigonometry in 11th grade, skill by skill

Unit circle, trig identities, and graphing trig functions. BAMS Academy breaks the unit into the skills below (part of all 11th grade math topics). Each comes with one of its practice questions.

Find a missing side of a right triangle using sine, cosine, or tangent

A right triangle has a hypotenuse of 15 and one acute angle of 30°. What is the length of the side OPPOSITE that angle (rounded to 2 decimal places)? (Choices: 30.00; 12.99; 7.50; 8.66.)

Answer: 7.50. Sin(30°) = opposite / hypotenuse, so opposite = hypotenuse × sin(30°) = 15 × sin(30°) ≈ 7.50.

A right triangle has a hypotenuse of 13 and one acute angle of 60°. What is the length of the side OPPOSITE that angle (rounded to 2 decimal places)? (Choices: 6.50; 22.52; 15.01; 11.26.)

Answer: 11.26. Sin(60°) = opposite / hypotenuse, so opposite = hypotenuse × sin(60°) = 13 × sin(60°) ≈ 11.26.

Find a missing angle of a right triangle using inverse trig functions

A right triangle has a side opposite an angle of length 7 and a hypotenuse of 14. What is the measure of that angle (rounded to 1 decimal place, in degrees)? (Choices: 40.0°; 30.0°; 60.0°; 0.5°.)

Answer: 30.0°. Sin(θ) = opposite / hypotenuse = 7 / 14. θ = sin⁻¹(7/14) ≈ 30.0°.

A right triangle has a side opposite an angle of length 6 and a hypotenuse of 12. What is the measure of that angle (rounded to 1 decimal place, in degrees)? (Choices: 0.5°; 40.0°; 30.0°; 60.0°.)

Answer: 30.0°. Sin(θ) = opposite / hypotenuse = 6 / 12. θ = sin⁻¹(6/12) ≈ 30.0°.

Evaluate sine and cosine of common unit-circle angles

On the unit circle, what is cos(90°) (as a decimal, rounded to 3 places)?

Answer: 0. Cos(90°) ≈ 0 on the unit circle.

On the unit circle, what is cos(0°) (as a decimal, rounded to 3 places)?

Answer: 1. Cos(0°) ≈ 1 on the unit circle.

Worked examples

Example 1

Question: A right triangle has a hypotenuse of 5 and one acute angle of 60°. What is the length of the side OPPOSITE that angle (rounded to 2 decimal places)?

1. 8.66
2. 4.33
3. 2.50
4. 5.77

How to solve it: Sin(60°) = opposite / hypotenuse, so opposite = hypotenuse × sin(60°) = 5 × sin(60°) ≈ 4.33.

Answer: 4.33

Why the other choices don't work:

• A student who picks "8.66" usually used tangent instead of sine.
• A student who picks "2.50" usually used cosine instead of sine.
• A student who picks "5.77" usually divided the hypotenuse by sine instead of multiplying.

Example 2

Question: A ladder leans against a wall, making a 60° angle with the ground. The base of the ladder is 5 feet from the wall. How tall up the wall does the ladder reach (rounded to 2 decimal places)?

1. 2.89 ft
2. 2.50 ft
3. 4.33 ft
4. 8.66 ft

How to solve it: Tan(60°) = opposite / adjacent, so height = adjacent × tan(60°) = 5 × tan(60°) ≈ 8.66 ft.

Answer: 8.66 ft

Why the other choices don't work:

• A student who picks "2.89 ft" usually divided the base distance by tangent instead of multiplying.
• A student who picks "2.50 ft" usually used cosine instead of tangent.
• A student who picks "4.33 ft" usually used sine instead of tangent.

Common mistakes to watch for

• Question: A right triangle has a hypotenuse of 14 and one acute angle of 60°. What is the length of the side ADJACENT to that angle (rounded to 2 decimal places)? (Choices: 7.00; 28.00; 12.12; 24.25.)

  Answer: 7.00.

  A student who picks "28.00" usually divided the hypotenuse by cosine instead of multiplying.

• Question: A right triangle has a hypotenuse of 10 and one acute angle of 30°. What is the length of the side ADJACENT to that angle (rounded to 2 decimal places)? (Choices: 8.66; 11.55; 5.77; 5.00.)

  Answer: 8.66.

  A student who picks "5.77" usually used tangent instead of cosine.

• Question: A right triangle has a side opposite an angle of length 7 and a hypotenuse of 14. What is the measure of that angle (rounded to 1 decimal place, in degrees)? (Choices: 40.0°; 30.0°; 60.0°; 0.5°.)

  Answer: 30.0°.

  A student who picks "0.5°" usually forgot to convert the result from radians to degrees.

• Question: A right triangle has a side opposite an angle of length 6 and a hypotenuse of 12. What is the measure of that angle (rounded to 1 decimal place, in degrees)? (Choices: 0.5°; 40.0°; 30.0°; 60.0°.)

  Answer: 30.0°.

  A student who picks "60.0°" usually used inverse cosine instead of inverse sine.

Try these practice questions

1. A ladder leans against a wall, making a 30° angle with the ground. The base of the ladder is 7 feet from the wall. How tall up the wall does the ladder reach (rounded to 2 decimal places)?

   1. 6.06 ft
   2. 12.12 ft
   3. 3.50 ft
   4. 4.04 ft

2. A right triangle has a hypotenuse of 14 and one acute angle of 60°. What is the length of the side ADJACENT to that angle (rounded to 2 decimal places)?

   1. 7.00
   2. 28.00
   3. 12.12
   4. 24.25

3. A ladder leans against a wall, making a 60° angle with the ground. The base of the ladder is 3 feet from the wall. How tall up the wall does the ladder reach (rounded to 2 decimal places)?

   1. 1.50 ft
   2. 2.60 ft
   3. 5.20 ft
   4. 1.73 ft

4. A right triangle has a hypotenuse of 10 and one acute angle of 30°. What is the length of the side ADJACENT to that angle (rounded to 2 decimal places)?

   1. 8.66
   2. 11.55
   3. 5.77
   4. 5.00

5. A ladder leans against a wall, making a 60° angle with the ground. The base of the ladder is 10 feet from the wall. How tall up the wall does the ladder reach (rounded to 2 decimal places)?

   1. 17.32 ft
   2. 8.66 ft
   3. 5.77 ft
   4. 5.00 ft

6. A ladder leans against a wall, making a 60° angle with the ground. The base of the ladder is 6 feet from the wall. How tall up the wall does the ladder reach (rounded to 2 decimal places)?

   1. 10.39 ft
   2. 5.20 ft
   3. 3.00 ft
   4. 3.46 ft

Answer key

1. 4.04 ft — Tan(30°) = opposite / adjacent, so height = adjacent × tan(30°) = 7 × tan(30°) ≈ 4.04 ft.
2. 7.00 — Cos(60°) = adjacent / hypotenuse, so adjacent = hypotenuse × cos(60°) = 14 × cos(60°) ≈ 7.00.
3. 5.20 ft — Tan(60°) = opposite / adjacent, so height = adjacent × tan(60°) = 3 × tan(60°) ≈ 5.20 ft.
4. 8.66 — Cos(30°) = adjacent / hypotenuse, so adjacent = hypotenuse × cos(30°) = 10 × cos(30°) ≈ 8.66.
5. 17.32 ft — Tan(60°) = opposite / adjacent, so height = adjacent × tan(60°) = 10 × tan(60°) ≈ 17.32 ft.
6. 10.39 ft — Tan(60°) = opposite / adjacent, so height = adjacent × tan(60°) = 6 × tan(60°) ≈ 10.39 ft.

Keep practicing

The fastest way to build confidence is a few questions at a time, with feedback on each answer. Start with Trigonometry practice for grade 11, where every question comes with a step-by-step explanation.

More from BAMS Academy:

• All 11th grade math topics
• Geometry practice
• Algebra II practice
• BAMS Academy math practice by grade
• Every 11th grade subject