Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 9: Some Applications of Trigonometry — notes
The chapter’s 8 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Why Trigonometry Is Used
Okay, so, trigonometry is a very old subject.
- • Trigonometry: used for heights & distances
- • Theodolite: measures angles (surveying)
- • Great Trigonometric Survey: discovered Mount Everest (1852)
- • Named after Sir George Everest (1856)
2. Line of Sight, Angle of Elevation and Angle of Depression
Okay, so let's talk about how we look at things — up or down.
- • Line of sight: eye to object viewed
- • Angle of elevation: line of sight above horizontal (looking up)
- • Angle of depression: line of sight below horizontal (looking down)
3. Finding the Height of the Minar — The Method
Okay, so suppose you want to find the height of a minar, without actually measuring it.
- • CD = CB + BD, where BD = AE (height of student)
- • Need BC: use tan A = BC/AB or cot A = AB/BC
- • Solve for BC, then height = BC + AE
4. Example: Height of a Tower (Single Angle of Elevation)
Okay, so let's see how this method works on an actual problem.
- • Tower AB, distance BC = 15 m, angle of elevation 60°
- • tan 60° = AB/BC
- • √3 = AB/15
- • AB = 15√3 m
5. Example: Ladder Problem (Using sin)
Okay, so let's look at this problem.
- • BD = AD − AB = 5 − 1.3 = 3.7 m
- • sin 60° = BD/BC → BC = 3.7 × 2/√3 = 4.28 m
- • cot 60° = DC/BD → DC = 3.7/√3 = 2.14 m
- • (take √3 = 1.73)
6. Example: Chimney with Observer's Height
Okay, so let's look at this one together.
- • Observer height = 1.5 m, distance DE = 28.5 m, angle 45°
- • tan 45° = AE/DE → 1 = AE/28.5
- • AE = 28.5 m
- • Height of chimney AB = AE + 1.5 = 30 m
7. Example: Flagstaff on a Building (Two Angles, Two Triangles)
Okay, so here's a nice one — a flagstaff on top of a building.
- • Building AB = 10 m, angle 30°; flagstaff top angle 45°
- • tan 30° = AB/AP → AP = 10√3 = 17.32 m
- • Let DB = x, AD = 10 + x
- • tan 45° = AD/AP → x = 10(√3 − 1) = 7.32 m
8. Example: Shadow Lengths at Two Sun Altitudes
Okay, so here's a nice one about a tower and its shadow.
- • AB = h, BC = x (shadow at 60°), DB = x+40 (shadow at 30°)
- • tan 60° = h/x → h = x√3
- • tan 30° = h/(x+40) → 3x = x + 40
- • x = 20, so h = 20√3 m
Summary
Okay, so let's look back at everything we did in this chapter. Trigonometry is a very old subject. It was first needed for astronomy, and surveyors used it too — in fact the Great Trigonometric Survey used it to discover Mount Everest. We use it to find heights and distances, without actually measuring them. We learned a few key ideas. The line of sight is the line from the observer's eye to the object. When we look up, above the horizontal, that angle is the angle of elevation. When we look down, below the horizontal, that's the angle of depression. Then we learned a method that works every time. First, draw the right triangle. Then, identify the known angle and sides. Then, choose the correct ratio — tan, cot, sin, or cos — to find the unknown side. We used this same method again and again. For the height of a tower. For the length of a ladder. For a chimney, where we added the observer's own height. For a flagstaff, using two right triangles together. And for a tower, using its shadow at two different times, when the Sun was at different heights in the sky. Notice something — in every single case, it was the known angle and sides that told us which ratio to pick. Once we picked the right one, solving the equation gave us the answer. So, tell me — out of all these examples, which one did you enjoy solving the most?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 9. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Some Applications of Trigonometry" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
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