Applying SOH CAH TOA: Practical Examples

This page demonstrates the practical application of SOH CAH TOA through two types of problems: calculating a length and calculating an angle in right-angled triangles. These examples illustrate how to use the trigonometric ratios in real-world scenarios.

Example: Calculating a length (AB) using tangent: Given: Angle ACB = 27°, BC = 4.5 cm Solution: tan(27°) = AB / 4.5 AB = 4.5 × tan(27°) AB ≈ 2.30 cm

This example shows how to use the tangent ratio when given an angle and the adjacent side to find the opposite side.

Example: Calculating an angle (BCA) using sine: Given: AB = 2.5 cm, AC = 4 cm Solution: sin(BCA) = 2.5 / 4 BCA = arcsin(2.5 / 4) BCA ≈ 39°

This example demonstrates how to use the sine ratio to find an unknown angle when given the opposite side and hypotenuse.

Highlight: These examples showcase the versatility of SOH CAH TOA in solving different types of trigonometric problems. Whether you need to find a missing side length or an unknown angle, these formulas provide a straightforward approach.

Understanding these applications is crucial for students learning trigonometry and for professionals in fields like engineering, architecture, and physics where precise calculations involving triangles are often required. Practicing with various examples helps reinforce the concepts and improves problem-solving skills in trigonometry.