Trigonometric Ratios and Triangle Calculations

Flashcards covering trigonometric ratios and triangle calculations from the lecture notes.

Trigonometric Ratios

Ratios relating the lengths of sides in a triangle to its angles.

$$\sin(\theta)$$

$$\frac{\text{Opposite side}}{\text{Hypotenuse}}$$

$$\cos(\theta)$$

$$\frac{\text{Adjacent side}}{\text{Hypotenuse}}$$

$$\tan(\theta)$$

$$\frac{\text{Opposite side}}{\text{Adjacent side}}$$

$$\cot(\theta)$$

$$\frac{\text{Adjacent side}}{\text{Opposite side}}$$

$$\csc(\theta)$$

$\frac{\text{Hypotenuse}}{\text{Opposite side}}$ or $\frac{1}{\sin(\theta)}$

Calculated Angle Measure $m\angle A$

$$m\angle A = 180^\circ - (82^\circ + 42^\circ) = 56^\circ$$

Calculated Side Length $a$

$$a = \frac{7 \times \sin(56^\circ)}{\sin(42^\circ)} \approx 8.67$$