Deciding the Trigonometric Rule Flashcards

All 6 cards in this deck

Which rule do you use to find the third side when you know two sides and the angle between them?

The cosine rule, $a^2=b^2+c^2-2bc\cos A$.

Which rule do you use to find an angle when you know all three sides?

The cosine rule, $\cos A=\dfrac{b^2+c^2-a^2}{2bc}$.

Which rule do you use when you know a side and the angle opposite it, plus one more side or angle?

The sine rule.

Which methods should you use in a triangle that contains a right angle?

Pythagoras' theorem and SOHCAHTOA.

They are quicker, though the sine and cosine rules would still work.

True or false? The cosine rule can find a missing side when you know two sides and a non-included angle.

False.

The angle must be the included angle; otherwise start with the sine rule.

What are the steps to solve a problem across two adjoining triangles?

e.g. triangles $ABC$ and $ADC$ share side $AC$; area of $ADC$ is known, $AB$ is required

1. Use the given information in the first triangle (here $\tfrac12 ab\sin C=$ area) to find its missing side.
2. Use the cosine (or sine) rule in that triangle to find the shared side $AC$.
3. Use the sine (or cosine) rule in the second triangle with $AC$ to find $AB$.