how is cos60 = 1/2

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