Chapter 6 · Kerala SSLC Class 10 Maths
Trigonometry
Two ways to learn — a crisp formula reference, or a story that makes angles feel real.
Real scenarios where trig ratios arise naturally — then the maths.
How story mode works
Each scene is a real situation where trigonometry solves a genuine problem — heights you cannot measure directly, angles you can only observe. The ratio emerges from the situation. Tap any dark panel to see the formal maths.
The Lighthouse
A sailor stands on the beach, exactly 100 metres from the base of a lighthouse. He looks up and sees the top of the lighthouse at an angle of elevation of 30°. How tall is the lighthouse?
The sailor cannot climb the lighthouse and drop a tape measure. But he has one angle and one distance. That is enough.
The sailor, the base of the lighthouse, and its top form a right triangle. The horizontal distance (100 m) is the adjacent side. The height is the opposite side. The angle at the sailor is 30°.
Which ratio connects opposite and adjacent? That would be tan.
tan 30° = opposite / adjacent
1/√3 = height / 100
height = 100 / √3 = 100√3 / 3 ≈ 57.7 m
The lighthouse is about 57.7 metres tall — measured from the beach with nothing but an angle. That is the power of trigonometry.
The Memory Trick
The standard angle values come up in almost every Kerala SSLC trig question. Instead of memorising a table, spot the pattern.
Write sin 0°, sin 30°, sin 45°, sin 60°, sin 90° as fractions with denominator 2. The numerators are √0, √1, √2, √3, √4 — in order.
sin 0° = √0/2 = 0
sin 30° = √1/2 = 1/2
sin 45° = √2/2 = 1/√2
sin 60° = √3/2
sin 90° = √4/2 = 1
For cos, read the same pattern backwards: cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, cos 90° = 0.
The Shadow Problem
A tree stands 12 metres tall. At a particular time of day it casts a shadow. The shadow is 12√3 metres long. What is the angle of elevation of the sun at that moment?
The tree is vertical — it is the opposite side. The shadow is horizontal — it is the adjacent side. The sun's rays form the hypotenuse. We want the angle θ at the tip of the shadow.
tan θ = opposite / adjacent
= 12 / (12√3)
= 1/√3
We know tan 30° = 1/√3. So θ = 30°.
We never needed a calculator — the answer came straight from the standard values table. The problem was designed so the numbers matched a known angle.
The Big Picture
Every Kerala SSLC trig question fits one of these patterns. Know these and Chapter 6 is done.
Find a side from angle + another side
Pick sin/cos/tan, substitute, solve
Find an angle from two sides
Compute ratio → match to standard table
Evaluate trig expression at standard angle
Use the √0,√1,√2,√3,√4 pattern
Simplify using identity
sin²θ + cos²θ = 1
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