01 · SOLVING APPROACH
3 Steps to Solve Single Triangle Questions
Step 1
Draw the ground level, height (vertical line), and line of sight to form △ABC with ∠B = 90°.
Step 2
Identify the given side and the side to find (Opposite, Adjacent, or Hypotenuse).
Step 3
Apply tan θ, sin θ, or cos θ and solve for the unknown side.
02 · SOLVED NCERT EXAMPLES
Step-by-Step Problem Solving
EXAMPLE 1 · TOWER HEIGHT
A tower stands vertically on ground. From a point 15 m away from foot, angle of elevation of top is 60°. Find height.
Let height of tower = h, distance from foot = 15 m, angle θ = 60°.
tan 60° = Opposite / Adjacent = h / 15
√3 = h / 15 ⟹ h = 15√3 metres
√3 = h / 15 ⟹ h = 15√3 metres
Height of tower is 15√3 m (≈ 25.98 m).
EXAMPLE 2 · BROKEN TREE PROBLEM
A tree breaks due to storm and broken top touches ground making an angle of 30°. Distance from foot to top on ground is 8 m. Find total height of tree.
Let unbroken part = h₁, broken slanting part = h₂. Distance = 8 m, θ = 30°.
tan 30° = h₁ / 8 ⟹ 1/√3 = h₁ / 8 ⟹ h₁ = 8 / √3
cos 30° = 8 / h₂ ⟹ √3/2 = 8 / h₂ ⟹ h₂ = 16 / √3
cos 30° = 8 / h₂ ⟹ √3/2 = 8 / h₂ ⟹ h₂ = 16 / √3
Total Height = h₁ + h₂ = 8/√3 + 16/√3 = 24/√3 = 8√3 metres.
03 · QUICK SUMMARY
Key Takeaways
01
When height and distance are involved, use tan θ = Height / Distance.
02
When slant length / string length is involved, use sin θ = Height / Slant Length.
03
Always rationalise denominators (e.g. 24/√3 = 8√3).