Revision sheet

Special right triangles

45-45-90: $1 : 1 : \sqrt{2}$. 30-60-90: $1 : \sqrt{3} : 2$.

Watch out: √2 vs √3.

Trigonometric ratios

SOH-CAH-TOA, for an acute angle of a right triangle.

Watch out: opposite and adjacent depend on which angle you look from.

Finding sides

Label → choose the ratio → solve (multiply or divide).

Watch out: the hypotenuse is the longest side; check your answer.

Finding angles

$A = \sin^{-1}$, $\cos^{-1}$ or $\tan^{-1}$ of the side ratio.

Watch out: inverse, not reciprocal; degree mode.

Complementary angles

$\sin x = \cos(90^\circ - x)$.

Watch out: equal values need complementary angles, not the same angle.

Area of any triangle

½ab sin C, with C between a and b.

Watch out: use the included angle.

Law of sines

a / sin A = b / sin B = c / sin C.

Watch out: pair each side with its opposite angle.

Law of cosines

c² = a² + b² − 2ab cos C.

Watch out: Pythagoras alone works only for a right angle.