🚀 StudyNest is growing. New lessons and worksheets are added regularly.
Final Checkpoint
Section A: Right-Triangle Skills
- State SOH CAH TOA.
- Find x if sin38°=x/14.
- Find θ if cosθ=9/12.
- Find the missing leg when hypotenuse=17 and other leg=8.
Section B: Applications
- A tree casts a 16 m horizontal line to an observer and has angle of elevation 41°. Find the height.
- A plane flies 50 km on bearing 040°. Find north and east components.
- Convert 62.6° to degrees and minutes.
Section C: Non-Right and 3D Triangles
- A=36°, a=7, B=81°. Find b.
- b=9, c=12, A=70°. Find a.
- Find the space diagonal of a cuboid 5×12×20.
✅ Check Your Work
Show answers and working
- sin=O/H, cos=A/H, tan=O/A.
- x=14sin38°≈8.62.
- θ=cos⁻¹(9/12)≈41.4°.
- x²=17²−8²=225, so x=15.
- h=16tan41°≈13.9 m.
- North=50cos40°≈38.3 km; east=50sin40°≈32.1 km.
- 0.6×60=36, so 62°36′.
- b=7sin81°/sin36°≈11.8.
- a²=9²+12²−2(9)(12)cos70°≈151.1, so a≈12.3.
- √(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
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.