Calculating Angles Using Trigonometric Ratios

This page demonstrates the inverse application of trigonometric ratios to find unknown angles in right-angled triangles.

Example: The page works through calculating angle BCA in a right-angled triangle:

• Given AB = 2.5 units
• Given AC = 4 units
• Using sine ratio: sin(BCA) = 2.5/4
• Solution: BCA = arcsin$2.5/4$ = 39°

Highlight: The use of inverse trigonometric functions (arcsin, arccos, arctan) is crucial for finding unknown angles.

Definition: Inverse trigonometric functions (arc functions) are used to find angles when side lengths are known.

Vocabulary:

• Arcsin: The inverse function of sine, used to find an angle when given the sine ratio
• Right angle: An angle of 90 degrees, characteristic of right-angled triangles

Understanding Basic Trigonometric Ratios

This page introduces the fundamental trigonometric ratios through the SOH-CAH-TOA mnemonic device. The content focuses on the relationship between angles and sides in right-angled triangles.

Definition: SOH-CAH-TOA represents the three main trigonometric ratios:

• Sine (SOH): opposite/hypotenuse
• Cosine (CAH): adjacent/hypotenuse
• Tangent (TOA): opposite/adjacent

Example: A practical application is demonstrated through calculating length AB in a right-angled triangle:

• Given angle = 27°
• Adjacent side (BC) = 4.5 cm
• Using tangent ratio: AB = 4.5 × tan(27°)
• Result: AB = 2.3 cm

Highlight: The page emphasizes the importance of correctly identifying the opposite, adjacent, and hypotenuse sides relative to the angle being considered.

Vocabulary:

• Hypotenuse: The longest side of a right-angled triangle, opposite to the right angle
• Adjacent: The side next to the angle being considered
• Opposite: The side opposite to the angle being considered