How to Find the Value of Sin 15 Degrees (Sin15°) Without Using Formula — Graphical Approach

Step 1: Prepare a right triangle ΔABC with one of its interior angles being 15°. From the definition of sin, the ratio of the opposite side (BC) to the hypotenuse (AC) of ΔABC is sin15°.
sin15° = BC/AC

Step 2: Inside ΔABC, construct a new triangle such that one of the interior angles is 60°.
∠DCB = 60°

Step 3: The sum of the interior angles of ΔABC is 180°, and as ∠CAB = 15° and ∠ABC = 90°, then
∠ACB = 180° − (15° + 90°) = 75°.
∴ ∠ACB = 75°

Step 4: Since ∠DCB = 60°, we have
∠ACD = ∠ACB − ∠DCB = 75° − 60° = 15°
∴ ∠ACD =15°