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Intermediate ∿ Trigonometry Topic 10 of 98

Solving Right Triangles

Find all sides and angles using ratios and the Pythagorean theorem.

Key idea

Find all sides and angles using ratios and the Pythagorean theorem.

In depth

To solve a triangle, find all unknown sides and angles. Use Pythagoras for sides, trig ratios when an angle is involved, and the angle sum 90° for the other acute angle.

Worked example

Legs 5 and 12: hypotenuse 13; angle A = tan⁻¹(5/12) ≈ 22.6°; angle B ≈ 67.4°.

Real-world uses

Common mistake

Rounding intermediate values, which introduces errors in later steps.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Solving Right Triangles?

Find all sides and angles using ratios and the Pythagorean theorem. It is a topic at the intermediate level in Trigonometry.

Where is Solving Right Triangles used in real life?

Real-world examples: Finding every side and angle of a roof truss or a triangular plot.

What should I learn before Solving Right Triangles?

Make sure you are comfortable with Reciprocal Trig Functions, the previous topic in Trigonometry.

What is a common mistake with Solving Right Triangles?

Rounding intermediate values, which introduces errors in later steps.

How can I practise Solving Right Triangles?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Solving Right Triangles?

Move on to Angles of Elevation and Depression next.

Related intermediate topics in Trigonometry