Grade 8 Trigonometric Ratios – VFIS.pptx

Trigonometry

1. Grade 8 – Trigonometric Ratios Vietnam-Finland International School (VFIS) Bright Classroom Edition

2. Learning Objectives • Define sine, cosine, and tangent. • Identify sides of a right triangle relative to an angle. • Use SOH-CAH-TOA to find missing sides or angles. • Apply trigonometric ratios to real-world problems.

3. Prior Knowledge Review • Identify parts of a right-angled triangle. • Recall Pythagoras' Theorem: a² + b² = c². Question: What is the hypotenuse in a right triangle?

4. Triangle Components Label triangle ABC: - Hypotenuse (longest side) - Opposite side (across from the angle) - Adjacent side (next to the angle)

5. Definition of Trigonometric Ratios sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent Mnemonic: SOH-CAH-TOA

6. Example 1 - Basic Evaluation Find the following: • sin 30° • cos 45° • tan 60° (Use degree mode on your calculator.)

7. Example 2 - Finding Missing Side A ladder 5 m long makes a 60° angle with the ground. Find the height of the ladder on the wall. Solution: sin 60 = h / 5 → h = 5 sin 60

8. Finding Missing Angles If sin θ = 0.8, find θ. Solution: θ = sin⁻¹(0.8) Use the inverse trig function on your calculator.

9. Real-World Applications • Measuring height of a building from its shadow. • Determining distance of a plane using radar angle. • Architecture and construction examples.

10. Common Errors • Mislabeling sides. • Using wrong trig function. • Calculator in radians instead of degrees. • Rounding too early.

11. Practice Tasks 1. Find x and y in right triangles with given angles. 2. Find θ when tan θ = 0.5. 3. A tree casts a 12 m shadow when the sun’s angle of elevation is 35°. Find the tree’s height.

12. Challenge Question A 10 m ramp rises to a platform 2 m high. Find: 1. The angle of elevation. 2. The horizontal distance covered.

13. Quick Quiz & Reflection 1. Which ratio involves adjacent and hypotenuse? 2. If tan 45 = 1, what does that imply about the triangle? 3. What mode should your calculator be in?

14. Summary SOH: sin = opposite / hypotenuse CAH: cos = adjacent / hypotenuse TOA: tan = opposite / adjacent Trigonometry connects geometry to real-world measurement.