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If A + B = 90° and Sin A = 3/5 find the value of tan B1. 3/42. 4/33. - 3/44. - 4/3 |
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Answer» Correct Answer - Option 2 : 4/3 Given: A + B = 90° and SinA = 3/5 Concept Used: Sinθ = Perpendicular/Hypotenuse tanθ = Perpendicular/Base Hypotenuse2 = Perpendicular2 + Base2 tan(90° - θ) = cotθ Calculation: SinA = 3/5 = Perpendicular/Hypotenuse ⇒ Perpendicular = 3k and Hypotenuse = 5k [Where, k is a constant] Base = √(Hypotenuse2 - Perpendicular) ⇒ Base = √(5k)2 - (3k)2 ⇒ Base = 4k tanA = Perpendicular/Base ⇒ tanA = 3k/4k = 3/4 ⇒ tan(90° - B) = 3/4 ⇒ cotB = 3/4 ⇒ tanB = 4/3 ∴ tanB = 4/3 |
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