Overview
This lecture covers the SOHCAHTOA method for solving right-angled triangle problems, explaining the relationships between sides and angles using trigonometric ratios.
SOHCAHTOA Method
- SOHCAHTOA is a mnemonic for choosing sine, cosine, or tangent based on triangle side information.
- In a right-angled triangle, the hypotenuse is the longest side, "opposite" is across from the angle, and "adjacent" is next to the angle.
Trigonometric Ratios
- Sine (sin) relates opposite side and hypotenuse: sin θ = opposite/hypotenuse.
- Cosine (cos) relates adjacent side and hypotenuse: cos θ = adjacent/hypotenuse.
- Tangent (tan) relates opposite side and adjacent side: tan θ = opposite/adjacent.
Worked Examples
- Example 1: Given opposite = 4, hypotenuse = 6, angle θ = sin⁻¹(4/6) = 41.8° (3 sig. fig).
- Example 2: Given opposite = 7, adjacent = 3, angle θ = tan⁻¹(7/3) = 66.8° (3 sig. fig).
- Example 3: Given adjacent = 3, angle = 55°, hypotenuse H = 3/cos55 = 5.23 (3 sig. fig).
- Example 4: Given hypotenuse = 5, angle = 23°, opposite O = 5 × sin23 = 1.95 (3 sig. fig).
Key Terms & Definitions
- SOHCAHTOA — mnemonic for sine, cosine, and tangent ratios in right-angled triangles.
- Hypotenuse — the longest side of a right-angled triangle, opposite the right angle.
- Opposite — the side across from the angle being considered.
- Adjacent — the side next to the angle being considered (but not the hypotenuse).
- Sine (sin) — ratio of opposite to hypotenuse.
- Cosine (cos) — ratio of adjacent to hypotenuse.
- Tangent (tan) — ratio of opposite to adjacent.
Action Items / Next Steps