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Assertion (A): sin 60° = . Reason (R): In an equilateral triangle of side 2, the altitude has length . Which is correct?

Class 10Introduction to TrigonometryTrigonometry
  • ABoth A and R are true and R is the correct explanation of A
  • BBoth A and R are true but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

An equilateral triangle of side 2 split by an altitude gives a 30-60-90 triangle with hypotenuse 2, base 1, altitude . So sin 60° = altitude/hyp = . R correctly explains A.
Answer: A) Both A and R are true and R is the correct explanation of A

Key idea: Why ratios — and not lengths

Two right triangles with the same acute angle θ are SIMILAR (Class 10 ch. 6 — AA criterion: both have a right angle and the angle θ).

Similar triangles → corresponding sides in fixed ratio.
So the ratio (opposite / hypotenuse) takes the SAME value in any right triangle with angle θ — regardless of how big the triangle is.

That's why sin θ, cos θ, tan θ are FUNCTIONS of the angle alone — they're well-defined.

This is the fundamental reason trigonometry works as a clean theory.

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