If sin 28° = 15/17 , then tan 62° = ?

Solution

sin 28° = 15/17 = perpendicular/hypotenuse So perpendicular = 15 & hypotenuse = 17 so base = 8 But for angle 62° which is complimentary of 28°, perpendicular = 8 & base = 15. So tan 62° = perpendicular/base = 8/15 Alternate Method sin 28° = 15/17 or cos (90°-28°) = 15/17 or cos 62° = 15/17 -----(1) Squaring on both sides, we will get cos² 62° = 225/289 or (1 - sin² 62°) = 225/289 or sin² 62° = 1 - 225/289 = 64/289 = `(8/17)^2` So sin 62° = 8/17 ----(2) Hence tan 62° = sin62°/cos62° = `(8/17)/(15/17)` = `8/15` ` ` ` ` ` ` ` ` ` ` ` `