Right Triangle Trigonometry — Trigonometry Unit 2 practice.
This unit covers SOH-CAH-TOA, solving right triangles and angles of elevation and depression — essential concepts for Trigonometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
Pick a mode. Play.
Answer questions as fast as you can. 2 minutes on the clock. Build streaks for bonus points!
Don't want to play?
Review the questions traditionally. Click to expand.
Questions loading...
Focus on understanding.
Focus on understanding core concepts before memorizing details. Use the game modes to test yourself repeatedly — spaced repetition is proven to boost long-term retention.
Related units
This unit covers SOH-CAH-TOA, solving right triangles and angles of elevation and depression — essential concepts for Trigonometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 SOH-CAH-TOA
Students must be able to identify the opposite, adjacent, and hypotenuse sides relative to a given angle in a right triangle. The three primary trig ratios — sine, cosine, and tangent — are defined by these side relationships. Memorizing SOH-CAH-TOA and applying it correctly is the foundation of every problem in this unit.
Key Points
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
- The hypotenuse is always opposite the right angle; 'opposite' and 'adjacent' are always defined relative to the angle in question, not the right angle
In a right triangle, angle A = 35°, and the hypotenuse = 10. Find the side opposite angle A.
Use SOH: sin(35°) = opposite / hypotenuse, so opposite = 10 × sin(35°). Evaluating: opposite = 10 × 0.5736 ≈ 5.74. Always identify which ratio connects your known values to your unknown before computing.
2 Solving Right Triangles
Solving a right triangle means finding all unknown side lengths and angle measures. Students must know when to use a trig ratio (given an angle and a side) versus the Pythagorean theorem (given two sides), and how to use inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to find missing angles.
Key Points
- Use inverse trig (e.g., θ = tan⁻¹(opposite/adjacent)) to find a missing angle when two sides are known
- The three angles of any triangle sum to 180°; in a right triangle the two acute angles sum to 90°
- You need at least one side length plus one other piece of information (a side or an acute angle) to fully solve a right triangle
- Round angles to the nearest tenth of a degree and sides to the nearest hundredth unless the problem specifies otherwise
A right triangle has legs of length 5 and 12. Find the hypotenuse and both acute angles.
First, find the hypotenuse using the Pythagorean theorem: c = √(5² + 12²) = √169 = 13. Next, find one acute angle: θ = tan⁻¹(5/12) ≈ 22.6°. The other acute angle is 90° − 22.6° = 67.4°, since the two acute angles must sum to 90°.
3 Angles Of Elevation And Depression
An angle of elevation is measured upward from the horizontal to a line of sight, while an angle of depression is measured downward from the horizontal. Both angles are always measured from a horizontal reference line, not from a vertical. Exam problems typically describe a real-world scenario and require students to draw and label a right triangle before applying trig.
Key Points
- Angle of elevation: observer looks UP — angle is between the horizontal and the line of sight
- Angle of depression: observer looks DOWN — angle is between the horizontal and the line of sight
- The angle of elevation from point A to point B equals the angle of depression from point B to point A (alternate interior angles)
- Always draw a diagram; correctly labeling opposite, adjacent, and hypotenuse relative to the given angle prevents setup errors
A person stands 50 m from the base of a building and measures the angle of elevation to the top as 62°. Find the height of the building.
The 50 m distance is the side adjacent to the 62° angle, and the building height is the opposite side, so use tangent: tan(62°) = height / 50. Solving: height = 50 × tan(62°) ≈ 50 × 1.8807 ≈ 94.0 m. Sketch the right triangle first to confirm which sides are opposite and adjacent before choosing the ratio.
Questions, answered.
What is Right Triangle Trigonometry?
Right Triangle Trigonometry is Unit 2 of Trigonometry, covering SOH-CAH-TOA, solving right triangles and angles of elevation and depression.
How to study for Trigonometry Unit 2?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.