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TRIGONOMETRY · LESSON 13

Trigonometry Final Checkpoint

Complete an exam-style assessment covering the full topic.

⏱️ 45–55 min 📘 Checkpoint 📐 Diagrams included

Final Checkpoint

Section A: Right-Triangle Skills

  1. State SOH CAH TOA.
  2. Find x if sin38°=x/14.
  3. Find θ if cosθ=9/12.
  4. Find the missing leg when hypotenuse=17 and other leg=8.

Section B: Applications

  1. A tree casts a 16 m horizontal line to an observer and has angle of elevation 41°. Find the height.
  2. A plane flies 50 km on bearing 040°. Find north and east components.
  3. Convert 62.6° to degrees and minutes.

Section C: Non-Right and 3D Triangles

  1. A=36°, a=7, B=81°. Find b.
  2. b=9, c=12, A=70°. Find a.
  3. Find the space diagonal of a cuboid 5×12×20.

✅ Check Your Work

Show answers and working
  1. sin=O/H, cos=A/H, tan=O/A.
  2. x=14sin38°≈8.62.
  3. θ=cos⁻¹(9/12)≈41.4°.
  4. x²=17²−8²=225, so x=15.
  5. h=16tan41°≈13.9 m.
  6. North=50cos40°≈38.3 km; east=50sin40°≈32.1 km.
  7. 0.6×60=36, so 62°36′.
  8. b=7sin81°/sin36°≈11.8.
  9. a²=9²+12²−2(9)(12)cos70°≈151.1, so a≈12.3.
  10. √(5²+12²+20²)=√569≈23.9.

🧭 Interactive Lab: Final Checkpoint Quiz

Change the values or make a choice and watch the mathematics respond.

📚 Lesson Wrap-Up

📘 Remember

  • Label the triangle before choosing a formula.
  • Use degree mode unless the question says otherwise.
  • Keep full calculator values until the final rounding step.

⚠️ Common Mistakes

  • Using the wrong reference angle.
  • Rounding too early.
  • Forgetting units or the degree symbol.

⭐ Exam Tips

  • Write the formula before substituting.
  • Sketch and label any diagram that is not already provided.
  • Check whether the answer is sensible for the shape.

🌍 Did You Know?

Surveyors, engineers, pilots and architects use trigonometry to calculate distances that are difficult or unsafe to measure directly.

Revision Guidance and Readiness