Pythagoras’ Theorem & Trigonometry

Pythagoras' theorem

$a^2+b^2=c^2$

Trigonometric ratios

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

TOA CAH SOH is applicable for only right-angled triangles

Obtuse angles

$\sin(180^\circ-\theta)=\sin\theta$
$\cos(180^\circ-\theta)=-\cos\theta$

Sine rule

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$

Cosine rule

$c^2=a^2+b^2-2 ab \cos C$

Area of triangle

$\text{Area of triangle}=\frac{1}{2}ab \sin C$

Bearings

A bearing is a 3-digit positive number with units of degree to show direction clockwise from the north direction.