Unit 1 Review and Quiz
A free Trigonometry lesson from the “Right Triangle Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews Right Triangle Trigonometry with a mix of computation, interpretation, and transfer problems.
What you'll learn
- Label right-triangle sides from a chosen angle
- Set up sine, cosine, tangent, and inverse-trig equations
- Compute side lengths, angles, heights, and distances
Worked example
Problem. Unit 1 Review and Quiz: A 30-degree angle has hypotenuse 60. Find the opposite side to the nearest tenth.
- Use sine because opposite and hypotenuse are involved.
- opposite = 60sin(30).
- Round at the end.
Answer: 30
Practice problems
1. Unit 1 Review and Quiz: For angle theta, opposite = 15 and hypotenuse = 39. Find sin(theta).
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 1 Review and Quiz: For angle theta, opposite = 15 and hypotenuse = 39. Find sin(theta).
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Sine is opposite over hypotenuse.
- Use 15/39.
- Simplify to 5/13.
- Check the result by substituting or estimating: the response should match 5/13 and make sense in the original problem.
Answer: 5/13
2. Unit 1 Review and Quiz: For angle theta, adjacent = 96 and hypotenuse = 100. Find cos(theta).
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 1 Review and Quiz: For angle theta, adjacent = 96 and hypotenuse = 100. Find cos(theta).
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Cosine is adjacent over hypotenuse.
- Use 96/100.
- Simplify to 24/25.
- Check the result by substituting or estimating: the response should match 24/25 and make sense in the original problem.
Answer: 24/25
3. Unit 1 Review and Quiz: For angle theta, opposite = 40 and adjacent = 75. Find tan(theta).
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 1 Review and Quiz: For angle theta, opposite = 40 and adjacent = 75. Find tan(theta).
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Tangent is opposite over adjacent.
- Use 40/75.
- Simplify to 8/15.
- Check the result by substituting or estimating: the response should match 8/15 and make sense in the original problem.
Answer: 8/15
4. Unit 1 Review and Quiz: A 30-degree angle has hypotenuse 60. Find the opposite side to the nearest tenth.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 1 Review and Quiz: A 30-degree angle has hypotenuse 60. Find the opposite side to the nearest tenth.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Use sine because opposite and hypotenuse are involved.
- opposite = 60sin(30).
- Round at the end.
- Check the result by substituting or estimating: the response should match 30 and make sense in the original problem.
Answer: 30
5. Unit 1 Review and Quiz: A 45-degree angle has adjacent side 12. Find the hypotenuse to the nearest tenth.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 1 Review and Quiz: A 45-degree angle has adjacent side 12. Find the hypotenuse to the nearest tenth.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Use cosine because adjacent and hypotenuse are involved.
- cos(theta) = adjacent/hypotenuse.
- Divide by cos(theta).
- Check the result by substituting or estimating: the response should match 17 and make sense in the original problem.
Answer: 17
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