Some Applications of Trigonometry — Lesson
1) Hook — A Real-Life Story to Spark Curiosity
Imagine you are standing at the base of the Qutub Minar in Delhi. You want to find out how tall this magnificent tower is without climbing it. How would you do that? Using just a protractor, a measuring tape, and some trigonometry, you can calculate its height from the ground! This is one of the exciting applications of trigonometry in daily life.
2) Core Concepts — Understanding Applications of Trigonometry
Trigonometry helps us find unknown heights and distances when direct measurement is difficult. It uses the relationships between the angles and sides of right-angled triangles.
| Scenario | What is Known? | What to Find? | Method |
|---|---|---|---|
| Height of a tower/building | Distance from tower (base), angle of elevation | Height of tower | Use tan θ = opposite/adjacent |
| Distance across a river | Two angles of depression/elevation from different points | Width of river | Apply trigonometric ratios and solve equations |
Example: A person stands 30 m away from a tree and measures the angle of elevation to the top of the tree as 45°. Find the height of the tree.
Solution: Let height of tree = h m.
Using tan θ = opposite/adjacent, we get
tan 45° = h / 30
Since tan 45° = 1,
1 = h / 30 ⇒ h = 30 m
Therefore, the tree is 30 m tall.
3) Key Formulas/Rules
For a right-angled triangle with angle θ, opposite side = O, adjacent side = A, hypotenuse = H:
- sin θ = O / H
- cos θ = A / H
- tan θ = O / A
In applications:
- Height = Distance × tan(angle of elevation)
- Distance = Height / tan(angle of elevation)
4) Did You Know?
Trigonometry was first developed by ancient Indian mathematicians like Aryabhata and Bhaskara II, who used sine tables to solve astronomical problems!
5) Exam Tips — Avoid These Common Mistakes
- Always identify the right angle triangle and label sides correctly (opposite, adjacent, hypotenuse) before applying formulas.
- Use the correct angle — angle of elevation is measured from the horizontal upward, angle of depression downward.
- Don’t confuse sin, cos, and tan — remember the mnemonic "Some People Have Curly Brown Hair" (S = Opp/Hyp, P = Adj/Hyp, H = Opp/Adj).
- Check your calculator mode — ensure it is set to degrees (not radians) when calculating trigonometric values.
- Practice solving word problems as CBSE often asks direct application questions in board exams.
Mission: Master This Topic!
Reinforce what you learned with fun activities
Ready to Battle? Test Your Knowledge!
Practice MCQs, build combos, climb the leaderboard!
Start Practice