Question
If sin 23° = `12/13` , then tan
67° = ?Solution
sin 23° = `12/13` = perpendicular/hypotenuse So perpendicular = 12 & hypotenuse = 13 so base = 5 But for angle 67° which is complimentary of 23°, perpendicular = 5 & base =12. So tan 67° = perpendicular/base = `5/12` Alternate Method sin 23° = `12/13` or cos (90°-23°) = `12/13` or cos 67° = `12/13` -----(1) Squaring on both sides, we will get cos2 67° = `144/169` or (1 - sin2 67°) = `144/169` or sin2 67° = 1 - `144/169` = `25/169` = `(5/13)^2` So sin 67° = `5/13` ----(2) Hence tan 67° = sin67°/cos67° = `(5/13)/(12/13)` = `5/12` ` ` ` ` ` ` ` ` ` ` ` `
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