how is cos60 = 1/2

Asked by Kaustav Sen | 19th Nov, 2010, 12:00: AM

Expert Answer:

Dear student
Consider the triangle PQR (drawing) with all three angles equal to 60°. By symmetry, all three sides are equal too (a more rigorous proof exists, but we skip it). Drop a line QS perpendicular to PR: it divides the big angle into two right-angled triangles with sharp angles of (30°, 60°), which is the kind we are interested in. By symmetry, the triangles are of equal size and shape ("congruent") and therefore (skipping another proof)

 

    SR = (1/2) PR

In the notation of the drawing

    a = (1/2) c

    a/c = 1/2 = sin 30° = cos 60°

 

 

 

 

 

 

 

We hope this clarifies your doubt.

Regards

Team

Topperlearning

Answered by  | 20th Nov, 2010, 07:27: PM

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