Unit 7 · 3 lessons

Trigonometry of Acute Triangles

Follow where the sine law and the cosine law come from, use them to find missing sides and angles in triangles with no right angle, and choose the right tool to solve real measurement problems.

29 practice questions
22 flashcards
3 interactive lessons

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Lessons

1The Sine LawDrawing an altitude splits any acute triangle into two right triangles, and writing the altitude two ways gives the sine law: $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ . Use it to find a side or an angle whenever you know an angle together with the side opposite it.Interactive10 questions
2The Cosine LawWhen you know two sides and the angle between them, or all three sides, the sine law has no complete pair to start from. The cosine law, $a^{2} = b^{2} + c^{2} - 2 b c cos A$ , fills the gap. It is the Pythagorean theorem with a correction term, and the correction is 0 when the angle is $9 0^{\circ}$ .Interactive9 questions
3Choosing a Method and Solving ProblemsReal problems don't arrive labelled. Sketch the triangle, mark what you know, and let the givens decide the tool: SOH CAH TOA for a right triangle, the sine law when you have an angle and its opposite side, the cosine law for SAS and SSS. Many problems chain two tools together.Interactive10 questions